5x-(x-2)=2x(x-5)

Solution for 5x-(x-2)=2x(x-5) equation:

Simplifying
5x + -1(x + -2) = 2x(x + -5)

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

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

Combine like terms: 5x + -1x = 4x
2 + 4x = 2x(x + -5)

Reorder the terms:
2 + 4x = 2x(-5 + x)
2 + 4x = (-5 * 2x + x * 2x)
2 + 4x = (-10x + 2x2)

Solving
2 + 4x = -10x + 2x2

Solving for variable 'x'.

Combine like terms: 4x + 10x = 14x
2 + 14x + -2x2 = -10x + 2x2 + 10x + -2x2

Reorder the terms:
2 + 14x + -2x2 = -10x + 10x + 2x2 + -2x2

Combine like terms: -10x + 10x = 0
2 + 14x + -2x2 = 0 + 2x2 + -2x2
2 + 14x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
2 + 14x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 7x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 7x + -1x2)' equal to zero and attempt to solve:

Simplifying
1 + 7x + -1x2 = 0

Solving
1 + 7x + -1x2 = 0

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

Divide each side by '-1'.
-1 + -7x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -7x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -7x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -7x + x2 = 0 + 1
-7x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-7x + x2 = 1

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 1 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + -7x + x2 = 13.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + -3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
x + -3.5 = 3.640054945

Simplifying
x + -3.5 = 3.640054945

Reorder the terms:
-3.5 + x = 3.640054945

Solving
-3.5 + x = 3.640054945

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 3.640054945 + 3.5
x = 3.640054945 + 3.5

Combine like terms: 3.640054945 + 3.5 = 7.140054945
x = 7.140054945

Simplifying
x = 7.140054945

Subproblem 2
x + -3.5 = -3.640054945

Simplifying
x + -3.5 = -3.640054945

Reorder the terms:
-3.5 + x = -3.640054945

Solving
-3.5 + x = -3.640054945

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -3.640054945 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -3.640054945 + 3.5
x = -3.640054945 + 3.5

Combine like terms: -3.640054945 + 3.5 = -0.140054945
x = -0.140054945

Simplifying
x = -0.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.140054945, -0.140054945}
Solution
x = {7.140054945, -0.140054945}