(4x-3)(-2x-2)=(-3+3x)2

Solution for (4x-3)(-2x-2)=(-3+3x)2 equation:

Simplifying
(4x + -3)(-2x + -2) = (-3 + 3x) * 2

Reorder the terms:
(-3 + 4x)(-2x + -2) = (-3 + 3x) * 2

Reorder the terms:
(-3 + 4x)(-2 + -2x) = (-3 + 3x) * 2

Multiply (-3 + 4x) * (-2 + -2x)
(-3(-2 + -2x) + 4x * (-2 + -2x)) = (-3 + 3x) * 2
((-2 * -3 + -2x * -3) + 4x * (-2 + -2x)) = (-3 + 3x) * 2
((6 + 6x) + 4x * (-2 + -2x)) = (-3 + 3x) * 2
(6 + 6x + (-2 * 4x + -2x * 4x)) = (-3 + 3x) * 2
(6 + 6x + (-8x + -8x2)) = (-3 + 3x) * 2

Combine like terms: 6x + -8x = -2x
(6 + -2x + -8x2) = (-3 + 3x) * 2

Reorder the terms for easier multiplication:
6 + -2x + -8x2 = 2(-3 + 3x)
6 + -2x + -8x2 = (-3 * 2 + 3x * 2)
6 + -2x + -8x2 = (-6 + 6x)

Solving
6 + -2x + -8x2 = -6 + 6x

Solving for variable 'x'.

Reorder the terms:
6 + 6 + -2x + -6x + -8x2 = -6 + 6x + 6 + -6x

Combine like terms: 6 + 6 = 12
12 + -2x + -6x + -8x2 = -6 + 6x + 6 + -6x

Combine like terms: -2x + -6x = -8x
12 + -8x + -8x2 = -6 + 6x + 6 + -6x

Reorder the terms:
12 + -8x + -8x2 = -6 + 6 + 6x + -6x

Combine like terms: -6 + 6 = 0
12 + -8x + -8x2 = 0 + 6x + -6x
12 + -8x + -8x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
12 + -8x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + -2x + -2x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + -2x + -2x2)' equal to zero and attempt to solve:

Simplifying
3 + -2x + -2x2 = 0

Solving
3 + -2x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-1.5 + x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x + x2 = 0 + 1.5
x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
x + x2 = 1.5

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 1.5 + 0.25

Combine like terms: 1.5 + 0.25 = 1.75
1.25 + x2 = 1.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
x + 0.5 = 1.322875656

Simplifying
x + 0.5 = 1.322875656

Reorder the terms:
0.5 + x = 1.322875656

Solving
0.5 + x = 1.322875656

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.322875656 + -0.5
x = 1.322875656 + -0.5

Combine like terms: 1.322875656 + -0.5 = 0.822875656
x = 0.822875656

Simplifying
x = 0.822875656

Subproblem 2
x + 0.5 = -1.322875656

Simplifying
x + 0.5 = -1.322875656

Reorder the terms:
0.5 + x = -1.322875656

Solving
0.5 + x = -1.322875656

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.322875656 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.322875656 + -0.5
x = -1.322875656 + -0.5

Combine like terms: -1.322875656 + -0.5 = -1.822875656
x = -1.822875656

Simplifying
x = -1.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.822875656, -1.822875656}
Solution
x = {0.822875656, -1.822875656}