36-2x(x-28)=-4(2x+56)

Solution for 36-2x(x-28)=-4(2x+56) equation:

Simplifying
36 + -2x(x + -28) = -4(2x + 56)

Reorder the terms:
36 + -2x(-28 + x) = -4(2x + 56)
36 + (-28 * -2x + x * -2x) = -4(2x + 56)
36 + (56x + -2x2) = -4(2x + 56)

Reorder the terms:
36 + 56x + -2x2 = -4(56 + 2x)
36 + 56x + -2x2 = (56 * -4 + 2x * -4)
36 + 56x + -2x2 = (-224 + -8x)

Solving
36 + 56x + -2x2 = -224 + -8x

Solving for variable 'x'.

Reorder the terms:
36 + 224 + 56x + 8x + -2x2 = -224 + -8x + 224 + 8x

Combine like terms: 36 + 224 = 260
260 + 56x + 8x + -2x2 = -224 + -8x + 224 + 8x

Combine like terms: 56x + 8x = 64x
260 + 64x + -2x2 = -224 + -8x + 224 + 8x

Reorder the terms:
260 + 64x + -2x2 = -224 + 224 + -8x + 8x

Combine like terms: -224 + 224 = 0
260 + 64x + -2x2 = 0 + -8x + 8x
260 + 64x + -2x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
260 + 64x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(130 + 32x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(130 + 32x + -1x2)' equal to zero and attempt to solve:

Simplifying
130 + 32x + -1x2 = 0

Solving
130 + 32x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-130 + -32x + x2 = 0

Move the constant term to the right:

Add '130' to each side of the equation.
-130 + -32x + 130 + x2 = 0 + 130

Reorder the terms:
-130 + 130 + -32x + x2 = 0 + 130

Combine like terms: -130 + 130 = 0
0 + -32x + x2 = 0 + 130
-32x + x2 = 0 + 130

Combine like terms: 0 + 130 = 130
-32x + x2 = 130

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = 130 + 256

Reorder the terms:
256 + -32x + x2 = 130 + 256

Combine like terms: 130 + 256 = 386
256 + -32x + x2 = 386

Factor a perfect square on the left side:
(x + -16)(x + -16) = 386

Calculate the square root of the right side: 19.646882704

Break this problem into two subproblems by setting 
(x + -16) equal to 19.646882704 and -19.646882704.

Subproblem 1
x + -16 = 19.646882704

Simplifying
x + -16 = 19.646882704

Reorder the terms:
-16 + x = 19.646882704

Solving
-16 + x = 19.646882704

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = 19.646882704 + 16

Combine like terms: -16 + 16 = 0
0 + x = 19.646882704 + 16
x = 19.646882704 + 16

Combine like terms: 19.646882704 + 16 = 35.646882704
x = 35.646882704

Simplifying
x = 35.646882704

Subproblem 2
x + -16 = -19.646882704

Simplifying
x + -16 = -19.646882704

Reorder the terms:
-16 + x = -19.646882704

Solving
-16 + x = -19.646882704

Solving for variable 'x'.

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

Add '16' to each side of the equation.
-16 + 16 + x = -19.646882704 + 16

Combine like terms: -16 + 16 = 0
0 + x = -19.646882704 + 16
x = -19.646882704 + 16

Combine like terms: -19.646882704 + 16 = -3.646882704
x = -3.646882704

Simplifying
x = -3.646882704

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.646882704, -3.646882704}
Solution
x = {35.646882704, -3.646882704}