diff --git a/Makefile b/Makefile
index 32b9af2..d4653d2 100644
--- a/Makefile
+++ b/Makefile
@@ -95,7 +95,7 @@ $(NAME): $(OBJS)
 
 run: $(NAME)
 	@echo $(YELLOW)"run"$(RESET)
-	@./$(NAME) "3 * x^2 + 1 * x^1 - 2 * x^0"
+	@./$(NAME) "3 * x^2 + 1 * x^1 - 2 * x^0 = 5 * x^1"
 
 clean:
 	$(RM_OBJS)
diff --git a/headers/computorv1.h b/headers/computorv1.h
index 3ed57d7..91f70cc 100644
--- a/headers/computorv1.h
+++ b/headers/computorv1.h
@@ -1,6 +1,4 @@
 #ifndef COMPUTORV1_H
 #define COMPUTORV1_H
 
-#include "libft.h"
-
 #endif
\ No newline at end of file
diff --git a/headers/lexer.h b/headers/lexer.h
index 84b5253..8402982 100644
--- a/headers/lexer.h
+++ b/headers/lexer.h
@@ -1,19 +1,16 @@
 #ifndef LEXER_H
 #define LEXER_H
 
-#include "../libft/includes/libft.h"
-
 typedef enum
 {
-    TOKEN_VARIABLE,       // x, y, etc.
-    TOKEN_NUMBER_INT,     // int
-    TOKEN_NUMBER_DOUBLE,  // double
-    TOKEN_POWER,          // ^ or **
-    TOKEN_PLUS,           // +
-    TOKEN_MINUS,          // -
-    TOKEN_MULTIPLICATION, // *
-    TOKEN_DIVISION,       // /
-    TOKEN_END             // null (end of input)
+    TOKEN_VARIABLE,      // x, y, etc.
+    TOKEN_NUMBER_INT,    // int
+    TOKEN_NUMBER_DOUBLE, // double
+    TOKEN_POWER,         // ^ or **
+    TOKEN_SIGN,          // + or -
+    TOKEN_FACTOR,        // * or /
+    TOKEN_EQUAL,         // =
+    TOKEN_END            // null (end of input)
 } token_type;
 
 typedef struct
diff --git a/src/computorv1.c b/src/computorv1.c
index 1aa490f..b425602 100644
--- a/src/computorv1.c
+++ b/src/computorv1.c
@@ -1,4 +1,5 @@
 #include "computorv1.h"
+#include "libft.h"
 #include "lexer.h"
 #include "errors.h"
 #include <stdio.h> // tmp for float debug
@@ -79,14 +80,12 @@ int main(int ac, char **av)
             ft_printf("%20s", "TOKEN_NUMBER_DOUBLE");
         if (tokens[i].type == TOKEN_POWER)
             ft_printf("%20s", "TOKEN_POWER");
-        if (tokens[i].type == TOKEN_PLUS)
-            ft_printf("%20s", "TOKEN_PLUS");
-        if (tokens[i].type == TOKEN_MINUS)
-            ft_printf("%20s", "TOKEN_MINUS");
-        if (tokens[i].type == TOKEN_MULTIPLICATION)
-            ft_printf("%20s", "TOKEN_MULTIPLICATION");
-        if (tokens[i].type == TOKEN_DIVISION)
-            ft_printf("%20s", "TOKEN_DIVISION");
+        if (tokens[i].type == TOKEN_SIGN)
+            ft_printf("%20s", "TOKEN_SIGN");
+        if (tokens[i].type == TOKEN_FACTOR)
+            ft_printf("%20s", "TOKEN_FACTOR");
+        if (tokens[i].type == TOKEN_EQUAL)
+            ft_printf("%20s", "TOKEN_EQUAL");
         if (tokens[i].type == TOKEN_END)
             ft_printf("%20s", "TOKEN_END");
 
diff --git a/src/lexer.c b/src/lexer.c
index 02b50f0..788f57c 100644
--- a/src/lexer.c
+++ b/src/lexer.c
@@ -1,8 +1,9 @@
 #include "lexer.h"
+#include "libft.h"
 #include "errors.h"
 #include <stdbool.h>
 
-// any single letter is a valid variable, like "x" or "y"
+// any single letter is a valid variable, like 'x' or 'y'
 static bool token_is_variable(const char *input, int input_pos, int *token_size)
 {
     if (ft_isalpha(input[input_pos]))
@@ -100,7 +101,7 @@ static bool token_is_number_double(const char *input, int input_pos, int *token_
     return true;
 }
 
-// power can be "^" and "**"
+// power can be '^' and "**"
 static bool token_is_power(const char *input, int input_pos, int *token_size)
 {
     if (input[input_pos] == '^')
@@ -116,10 +117,10 @@ static bool token_is_power(const char *input, int input_pos, int *token_size)
     return false;
 }
 
-// detect a single "+" is valid
-static bool token_is_plus(const char *input, int input_pos, int *token_size)
+// sign can be '+' or '-'
+static bool token_is_sign(const char *input, int input_pos, int *token_size)
 {
-    if (input[input_pos] == '+')
+    if (input[input_pos] == '+' || input[input_pos] == '-')
     {
         *token_size = 1;
         return true;
@@ -127,10 +128,10 @@ static bool token_is_plus(const char *input, int input_pos, int *token_size)
     return false;
 }
 
-// detect a single "-"
-static bool token_is_minus(const char *input, int input_pos, int *token_size)
+// factor can be '*' or '/' or ':'
+static bool token_is_factor(const char *input, int input_pos, int *token_size)
 {
-    if (input[input_pos] == '-')
+    if (input[input_pos] == '*' || input[input_pos] == '/' || input[input_pos] == ':')
     {
         *token_size = 1;
         return true;
@@ -138,21 +139,10 @@ static bool token_is_minus(const char *input, int input_pos, int *token_size)
     return false;
 }
 
-// detect a single "*"
-static bool token_is_multiplication(const char *input, int input_pos, int *token_size)
+// detect a single '='
+static bool token_is_equal(const char *input, int input_pos, int *token_size)
 {
-    if (input[input_pos] == '*')
-    {
-        *token_size = 1;
-        return true;
-    }
-    return false;
-}
-
-// detect a single "/"
-static bool token_is_division(const char *input, int input_pos, int *token_size)
-{
-    if (input[input_pos] == '+')
+    if (input[input_pos] == '=')
     {
         *token_size = 1;
         return true;
@@ -200,25 +190,20 @@ void lexerize(const char *input, token *tokens)
             tokens[token_count].type = TOKEN_POWER;
             tokens[token_count].value_char = '^';
         }
-        else if (token_is_plus(input, input_pos, &token_size))
+        else if (token_is_sign(input, input_pos, &token_size))
         {
-            tokens[token_count].type = TOKEN_PLUS;
-            tokens[token_count].value_char = '+';
+            tokens[token_count].type = TOKEN_SIGN;
+            tokens[token_count].value_char = input[input_pos];
         }
-        else if (token_is_minus(input, input_pos, &token_size))
+        else if (token_is_factor(input, input_pos, &token_size))
         {
-            tokens[token_count].type = TOKEN_MINUS;
-            tokens[token_count].value_char = '-';
+            tokens[token_count].type = TOKEN_FACTOR;
+            tokens[token_count].value_char = input[input_pos];
         }
-        else if (token_is_multiplication(input, input_pos, &token_size))
+        else if (token_is_equal(input, input_pos, &token_size))
         {
-            tokens[token_count].type = TOKEN_MULTIPLICATION;
-            tokens[token_count].value_char = '*';
-        }
-        else if (token_is_division(input, input_pos, &token_size))
-        {
-            tokens[token_count].type = TOKEN_DIVISION;
-            tokens[token_count].value_char = '/';
+            tokens[token_count].type = TOKEN_EQUAL;
+            tokens[token_count].value_char = '=';
         }
         else
         {