2(3x+2)(3x-2)-3(2x-1)(2x-1)=0

Solution for 2(3x+2)(3x-2)-3(2x-1)(2x-1)=0 equation:

Simplifying
2(3x + 2)(3x + -2) + -3(2x + -1)(2x + -1) = 0

Reorder the terms:
2(2 + 3x)(3x + -2) + -3(2x + -1)(2x + -1) = 0

Reorder the terms:
2(2 + 3x)(-2 + 3x) + -3(2x + -1)(2x + -1) = 0

Multiply (2 + 3x) * (-2 + 3x)
2(2(-2 + 3x) + 3x * (-2 + 3x)) + -3(2x + -1)(2x + -1) = 0
2((-2 * 2 + 3x * 2) + 3x * (-2 + 3x)) + -3(2x + -1)(2x + -1) = 0
2((-4 + 6x) + 3x * (-2 + 3x)) + -3(2x + -1)(2x + -1) = 0
2(-4 + 6x + (-2 * 3x + 3x * 3x)) + -3(2x + -1)(2x + -1) = 0
2(-4 + 6x + (-6x + 9x2)) + -3(2x + -1)(2x + -1) = 0

Combine like terms: 6x + -6x = 0
2(-4 + 0 + 9x2) + -3(2x + -1)(2x + -1) = 0
2(-4 + 9x2) + -3(2x + -1)(2x + -1) = 0
(-4 * 2 + 9x2 * 2) + -3(2x + -1)(2x + -1) = 0
(-8 + 18x2) + -3(2x + -1)(2x + -1) = 0

Reorder the terms:
-8 + 18x2 + -3(-1 + 2x)(2x + -1) = 0

Reorder the terms:
-8 + 18x2 + -3(-1 + 2x)(-1 + 2x) = 0

Multiply (-1 + 2x) * (-1 + 2x)
-8 + 18x2 + -3(-1(-1 + 2x) + 2x * (-1 + 2x)) = 0
-8 + 18x2 + -3((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) = 0
-8 + 18x2 + -3((1 + -2x) + 2x * (-1 + 2x)) = 0
-8 + 18x2 + -3(1 + -2x + (-1 * 2x + 2x * 2x)) = 0
-8 + 18x2 + -3(1 + -2x + (-2x + 4x2)) = 0

Combine like terms: -2x + -2x = -4x
-8 + 18x2 + -3(1 + -4x + 4x2) = 0
-8 + 18x2 + (1 * -3 + -4x * -3 + 4x2 * -3) = 0
-8 + 18x2 + (-3 + 12x + -12x2) = 0

Reorder the terms:
-8 + -3 + 12x + 18x2 + -12x2 = 0

Combine like terms: -8 + -3 = -11
-11 + 12x + 18x2 + -12x2 = 0

Combine like terms: 18x2 + -12x2 = 6x2
-11 + 12x + 6x2 = 0

Solving
-11 + 12x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-1.833333333 + 2x + x2 = 0

Move the constant term to the right:

Add '1.833333333' to each side of the equation.
-1.833333333 + 2x + 1.833333333 + x2 = 0 + 1.833333333

Reorder the terms:
-1.833333333 + 1.833333333 + 2x + x2 = 0 + 1.833333333

Combine like terms: -1.833333333 + 1.833333333 = 0.000000000
0.000000000 + 2x + x2 = 0 + 1.833333333
2x + x2 = 0 + 1.833333333

Combine like terms: 0 + 1.833333333 = 1.833333333
2x + x2 = 1.833333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 1.833333333 + 1

Reorder the terms:
1 + 2x + x2 = 1.833333333 + 1

Combine like terms: 1.833333333 + 1 = 2.833333333
1 + 2x + x2 = 2.833333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 2.833333333

Calculate the square root of the right side: 1.683250823

Break this problem into two subproblems by setting 
(x + 1) equal to 1.683250823 and -1.683250823.

Subproblem 1
x + 1 = 1.683250823

Simplifying
x + 1 = 1.683250823

Reorder the terms:
1 + x = 1.683250823

Solving
1 + x = 1.683250823

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.683250823 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.683250823 + -1
x = 1.683250823 + -1

Combine like terms: 1.683250823 + -1 = 0.683250823
x = 0.683250823

Simplifying
x = 0.683250823

Subproblem 2
x + 1 = -1.683250823

Simplifying
x + 1 = -1.683250823

Reorder the terms:
1 + x = -1.683250823

Solving
1 + x = -1.683250823

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.683250823 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.683250823 + -1
x = -1.683250823 + -1

Combine like terms: -1.683250823 + -1 = -2.683250823
x = -2.683250823

Simplifying
x = -2.683250823

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.683250823, -2.683250823}