(2x-3)2-4(x-6)(x+2)=-3

Solution for (2x-3)2-4(x-6)(x+2)=-3 equation:

Simplifying
(2x + -3) * 2 + -4(x + -6)(x + 2) = -3

Reorder the terms:
(-3 + 2x) * 2 + -4(x + -6)(x + 2) = -3

Reorder the terms for easier multiplication:
2(-3 + 2x) + -4(x + -6)(x + 2) = -3
(-3 * 2 + 2x * 2) + -4(x + -6)(x + 2) = -3
(-6 + 4x) + -4(x + -6)(x + 2) = -3

Reorder the terms:
-6 + 4x + -4(-6 + x)(x + 2) = -3

Reorder the terms:
-6 + 4x + -4(-6 + x)(2 + x) = -3

Multiply (-6 + x) * (2 + x)
-6 + 4x + -4(-6(2 + x) + x(2 + x)) = -3
-6 + 4x + -4((2 * -6 + x * -6) + x(2 + x)) = -3
-6 + 4x + -4((-12 + -6x) + x(2 + x)) = -3
-6 + 4x + -4(-12 + -6x + (2 * x + x * x)) = -3
-6 + 4x + -4(-12 + -6x + (2x + x2)) = -3

Combine like terms: -6x + 2x = -4x
-6 + 4x + -4(-12 + -4x + x2) = -3
-6 + 4x + (-12 * -4 + -4x * -4 + x2 * -4) = -3
-6 + 4x + (48 + 16x + -4x2) = -3

Reorder the terms:
-6 + 48 + 4x + 16x + -4x2 = -3

Combine like terms: -6 + 48 = 42
42 + 4x + 16x + -4x2 = -3

Combine like terms: 4x + 16x = 20x
42 + 20x + -4x2 = -3

Solving
42 + 20x + -4x2 = -3

Solving for variable 'x'.

Reorder the terms:
42 + 3 + 20x + -4x2 = -3 + 3

Combine like terms: 42 + 3 = 45
45 + 20x + -4x2 = -3 + 3

Combine like terms: -3 + 3 = 0
45 + 20x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-11.25 + -5x + x2 = 0

Move the constant term to the right:

Add '11.25' to each side of the equation.
-11.25 + -5x + 11.25 + x2 = 0 + 11.25

Reorder the terms:
-11.25 + 11.25 + -5x + x2 = 0 + 11.25

Combine like terms: -11.25 + 11.25 = 0.00
0.00 + -5x + x2 = 0 + 11.25
-5x + x2 = 0 + 11.25

Combine like terms: 0 + 11.25 = 11.25
-5x + x2 = 11.25

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 11.25 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 11.25 + 6.25

Combine like terms: 11.25 + 6.25 = 17.5
6.25 + -5x + x2 = 17.5

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 17.5

Calculate the square root of the right side: 4.183300133

Break this problem into two subproblems by setting 
(x + -2.5) equal to 4.183300133 and -4.183300133.

Subproblem 1
x + -2.5 = 4.183300133

Simplifying
x + -2.5 = 4.183300133

Reorder the terms:
-2.5 + x = 4.183300133

Solving
-2.5 + x = 4.183300133

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 4.183300133 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 4.183300133 + 2.5
x = 4.183300133 + 2.5

Combine like terms: 4.183300133 + 2.5 = 6.683300133
x = 6.683300133

Simplifying
x = 6.683300133

Subproblem 2
x + -2.5 = -4.183300133

Simplifying
x + -2.5 = -4.183300133

Reorder the terms:
-2.5 + x = -4.183300133

Solving
-2.5 + x = -4.183300133

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -4.183300133 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -4.183300133 + 2.5
x = -4.183300133 + 2.5

Combine like terms: -4.183300133 + 2.5 = -1.683300133
x = -1.683300133

Simplifying
x = -1.683300133

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.683300133, -1.683300133}