To solve this problem, we need to determine the value of x, which will satisfy the given equation and make the smallest possible value of 2a + 1 equal to 0.
We have the equation:
$6a^2 + 5a + x = 3
To find the value of x, we need to substitute 2a + 1 for a in the equation:
$6(2a + 1)^2 + 5(2a + 1) + x = 3
Simplifying the equation:
$6(4a^2 + 4a + 1) + 10a + 5 + x = 3
$24a^2 + 24a + 6 + 10a + 5 + x = 3
$24a^2 + 34a + 11 + x = 3
To make the smallest possible value of 2a + 1 equal to 0, we need to set a equal to -1/2:
$24(-1/2)^2 + 34(-1/2) + 11 + x = 3
$24(1/4) - 34/2 + 11 + x = 3
$6 - 17 + 11 + x = 3
To simplify the equation:
$6 - 17 + 11 + x = 3
$-1 + x = 3
To solve for x, we add 1 to both sides of the equation:
$-1 + x + 1 = 3 + 1
x = 4
The value of x is 4.
The answer is: 4
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
If $6a^2 + 5a + X = 3, The smallest possible value of $2a + 1$ is 0. What is the value of unknown variable X?

### Answer:
