(2x-1)(3x+2)=3

Solution for (2x-1)(3x+2)=3 equation:

Simplifying
(2x + -1)(3x + 2) = 3

Reorder the terms:
(-1 + 2x)(3x + 2) = 3

Reorder the terms:
(-1 + 2x)(2 + 3x) = 3

Multiply (-1 + 2x) * (2 + 3x)
(-1(2 + 3x) + 2x * (2 + 3x)) = 3
((2 * -1 + 3x * -1) + 2x * (2 + 3x)) = 3
((-2 + -3x) + 2x * (2 + 3x)) = 3
(-2 + -3x + (2 * 2x + 3x * 2x)) = 3
(-2 + -3x + (4x + 6x2)) = 3

Combine like terms: -3x + 4x = 1x
(-2 + 1x + 6x2) = 3

Solving
-2 + 1x + 6x2 = 3

Solving for variable 'x'.

Reorder the terms:
-2 + -3 + 1x + 6x2 = 3 + -3

Combine like terms: -2 + -3 = -5
-5 + 1x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-5 + 1x + 6x2 = 0

Factor a trinomial.
(-1 + -1x)(5 + -6x) = 0

Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + -1x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1x = 0 + 1
-1x = 0 + 1

Combine like terms: 0 + 1 = 1
-1x = 1

Divide each side by '-1'.
x = -1

Simplifying
x = -1
Subproblem 2
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
Solution
x = {-1, 0.8333333333}