x-(10-2x)=4x(x+5)

Solution for x-(10-2x)=4x(x+5) equation:

Simplifying
x + -1(10 + -2x) = 4x(x + 5)
x + (10 * -1 + -2x * -1) = 4x(x + 5)
x + (-10 + 2x) = 4x(x + 5)

Reorder the terms:
-10 + x + 2x = 4x(x + 5)

Combine like terms: x + 2x = 3x
-10 + 3x = 4x(x + 5)

Reorder the terms:
-10 + 3x = 4x(5 + x)
-10 + 3x = (5 * 4x + x * 4x)
-10 + 3x = (20x + 4x2)

Solving
-10 + 3x = 20x + 4x2

Solving for variable 'x'.

Combine like terms: 3x + -20x = -17x
-10 + -17x + -4x2 = 20x + 4x2 + -20x + -4x2

Reorder the terms:
-10 + -17x + -4x2 = 20x + -20x + 4x2 + -4x2

Combine like terms: 20x + -20x = 0
-10 + -17x + -4x2 = 0 + 4x2 + -4x2
-10 + -17x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-10 + -17x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 17x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + 17x + 4x2)' equal to zero and attempt to solve:

Simplifying
10 + 17x + 4x2 = 0

Solving
10 + 17x + 4x2 = 0

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

Divide each side by '4'.
2.5 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4.25x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4.25x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4.25x + x2 = 0 + -2.5
4.25x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
4.25x + x2 = -2.5

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = -2.5 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -2.5 + 4.515625

Combine like terms: -2.5 + 4.515625 = 2.015625
4.515625 + 4.25x + x2 = 2.015625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(x + 2.125) equal to 1.419727086 and -1.419727086.

Subproblem 1
x + 2.125 = 1.419727086

Simplifying
x + 2.125 = 1.419727086

Reorder the terms:
2.125 + x = 1.419727086

Solving
2.125 + x = 1.419727086

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 1.419727086 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 1.419727086 + -2.125
x = 1.419727086 + -2.125

Combine like terms: 1.419727086 + -2.125 = -0.705272914
x = -0.705272914

Simplifying
x = -0.705272914

Subproblem 2
x + 2.125 = -1.419727086

Simplifying
x + 2.125 = -1.419727086

Reorder the terms:
2.125 + x = -1.419727086

Solving
2.125 + x = -1.419727086

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -1.419727086 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -1.419727086 + -2.125
x = -1.419727086 + -2.125

Combine like terms: -1.419727086 + -2.125 = -3.544727086
x = -3.544727086

Simplifying
x = -3.544727086

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.705272914, -3.544727086}
Solution
x = {-0.705272914, -3.544727086}