-5(1-5x)5(-8x-2)=4x-8

Solution for -5(1-5x)5(-8x-2)=4x-8 equation:

Simplifying
-5(1 + -5x) * 5(-8x + -2) = 4x + -8

Reorder the terms:
-5(1 + -5x) * 5(-2 + -8x) = 4x + -8

Reorder the terms for easier multiplication:
-5 * 5(1 + -5x)(-2 + -8x) = 4x + -8

Multiply -5 * 5
-25(1 + -5x)(-2 + -8x) = 4x + -8

Multiply (1 + -5x) * (-2 + -8x)
-25(1(-2 + -8x) + -5x * (-2 + -8x)) = 4x + -8
-25((-2 * 1 + -8x * 1) + -5x * (-2 + -8x)) = 4x + -8
-25((-2 + -8x) + -5x * (-2 + -8x)) = 4x + -8
-25(-2 + -8x + (-2 * -5x + -8x * -5x)) = 4x + -8
-25(-2 + -8x + (10x + 40x2)) = 4x + -8

Combine like terms: -8x + 10x = 2x
-25(-2 + 2x + 40x2) = 4x + -8
(-2 * -25 + 2x * -25 + 40x2 * -25) = 4x + -8
(50 + -50x + -1000x2) = 4x + -8

Reorder the terms:
50 + -50x + -1000x2 = -8 + 4x

Solving
50 + -50x + -1000x2 = -8 + 4x

Solving for variable 'x'.

Reorder the terms:
50 + 8 + -50x + -4x + -1000x2 = -8 + 4x + 8 + -4x

Combine like terms: 50 + 8 = 58
58 + -50x + -4x + -1000x2 = -8 + 4x + 8 + -4x

Combine like terms: -50x + -4x = -54x
58 + -54x + -1000x2 = -8 + 4x + 8 + -4x

Reorder the terms:
58 + -54x + -1000x2 = -8 + 8 + 4x + -4x

Combine like terms: -8 + 8 = 0
58 + -54x + -1000x2 = 0 + 4x + -4x
58 + -54x + -1000x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
58 + -54x + -1000x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -27x + -500x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(29 + -27x + -500x2)' equal to zero and attempt to solve:

Simplifying
29 + -27x + -500x2 = 0

Solving
29 + -27x + -500x2 = 0

Begin completing the square.  Divide all terms by
-500 the coefficient of the squared term: 

Divide each side by '-500'.
-0.058 + 0.054x + x2 = 0.00

Move the constant term to the right:

Add '0.058' to each side of the equation.
-0.058 + 0.054x + 0.058 + x2 = 0.00 + 0.058

Reorder the terms:
-0.058 + 0.058 + 0.054x + x2 = 0.00 + 0.058

Combine like terms: -0.058 + 0.058 = 0.000
0.000 + 0.054x + x2 = 0.00 + 0.058
0.054x + x2 = 0.00 + 0.058

Combine like terms: 0.00 + 0.058 = 0.058
0.054x + x2 = 0.058

The x term is 0.054x.  Take half its coefficient (0.027).
Square it (0.000729) and add it to both sides.

Add '0.000729' to each side of the equation.
0.054x + 0.000729 + x2 = 0.058 + 0.000729

Reorder the terms:
0.000729 + 0.054x + x2 = 0.058 + 0.000729

Combine like terms: 0.058 + 0.000729 = 0.058729
0.000729 + 0.054x + x2 = 0.058729

Factor a perfect square on the left side:
(x + 0.027)(x + 0.027) = 0.058729

Calculate the square root of the right side: 0.242340669

Break this problem into two subproblems by setting 
(x + 0.027) equal to 0.242340669 and -0.242340669.

Subproblem 1
x + 0.027 = 0.242340669

Simplifying
x + 0.027 = 0.242340669

Reorder the terms:
0.027 + x = 0.242340669

Solving
0.027 + x = 0.242340669

Solving for variable 'x'.

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

Add '-0.027' to each side of the equation.
0.027 + -0.027 + x = 0.242340669 + -0.027

Combine like terms: 0.027 + -0.027 = 0.000
0.000 + x = 0.242340669 + -0.027
x = 0.242340669 + -0.027

Combine like terms: 0.242340669 + -0.027 = 0.215340669
x = 0.215340669

Simplifying
x = 0.215340669

Subproblem 2
x + 0.027 = -0.242340669

Simplifying
x + 0.027 = -0.242340669

Reorder the terms:
0.027 + x = -0.242340669

Solving
0.027 + x = -0.242340669

Solving for variable 'x'.

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

Add '-0.027' to each side of the equation.
0.027 + -0.027 + x = -0.242340669 + -0.027

Combine like terms: 0.027 + -0.027 = 0.000
0.000 + x = -0.242340669 + -0.027
x = -0.242340669 + -0.027

Combine like terms: -0.242340669 + -0.027 = -0.269340669
x = -0.269340669

Simplifying
x = -0.269340669

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.215340669, -0.269340669}
Solution
x = {0.215340669, -0.269340669}