-2x(2x+3)=4x+4-8

Solution for -2x(2x+3)=4x+4-8 equation:

Simplifying
-2x(2x + 3) = 4x + 4 + -8

Reorder the terms:
-2x(3 + 2x) = 4x + 4 + -8
(3 * -2x + 2x * -2x) = 4x + 4 + -8
(-6x + -4x2) = 4x + 4 + -8

Reorder the terms:
-6x + -4x2 = 4 + -8 + 4x

Combine like terms: 4 + -8 = -4
-6x + -4x2 = -4 + 4x

Solving
-6x + -4x2 = -4 + 4x

Solving for variable 'x'.

Reorder the terms:
4 + -6x + -4x + -4x2 = -4 + 4x + 4 + -4x

Combine like terms: -6x + -4x = -10x
4 + -10x + -4x2 = -4 + 4x + 4 + -4x

Reorder the terms:
4 + -10x + -4x2 = -4 + 4 + 4x + -4x

Combine like terms: -4 + 4 = 0
4 + -10x + -4x2 = 0 + 4x + -4x
4 + -10x + -4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
4 + -10x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(2 + -5x + -2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(2 + -5x + -2x2)' equal to zero and attempt to solve:

Simplifying
2 + -5x + -2x2 = 0

Solving
2 + -5x + -2x2 = 0

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

Divide each side by '-2'.
-1 + 2.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 2.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2.5x + x2 = 0 + 1
2.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
2.5x + x2 = 1

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 1 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 1 + 1.5625

Combine like terms: 1 + 1.5625 = 2.5625
1.5625 + 2.5x + x2 = 2.5625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.5625

Calculate the square root of the right side: 1.600781059

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.600781059 and -1.600781059.

Subproblem 1
x + 1.25 = 1.600781059

Simplifying
x + 1.25 = 1.600781059

Reorder the terms:
1.25 + x = 1.600781059

Solving
1.25 + x = 1.600781059

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = 1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 1.600781059 + -1.25
x = 1.600781059 + -1.25

Combine like terms: 1.600781059 + -1.25 = 0.350781059
x = 0.350781059

Simplifying
x = 0.350781059

Subproblem 2
x + 1.25 = -1.600781059

Simplifying
x + 1.25 = -1.600781059

Reorder the terms:
1.25 + x = -1.600781059

Solving
1.25 + x = -1.600781059

Solving for variable 'x'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + x = -1.600781059 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -1.600781059 + -1.25
x = -1.600781059 + -1.25

Combine like terms: -1.600781059 + -1.25 = -2.850781059
x = -2.850781059

Simplifying
x = -2.850781059

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.350781059, -2.850781059}
Solution
x = {0.350781059, -2.850781059}