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

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

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

Reorder the terms:
-5x(-5 + 2x) + -1x = -4(x + -2)
(-5 * -5x + 2x * -5x) + -1x = -4(x + -2)
(25x + -10x2) + -1x = -4(x + -2)

Reorder the terms:
25x + -1x + -10x2 = -4(x + -2)

Combine like terms: 25x + -1x = 24x
24x + -10x2 = -4(x + -2)

Reorder the terms:
24x + -10x2 = -4(-2 + x)
24x + -10x2 = (-2 * -4 + x * -4)
24x + -10x2 = (8 + -4x)

Solving
24x + -10x2 = 8 + -4x

Solving for variable 'x'.

Reorder the terms:
-8 + 24x + 4x + -10x2 = 8 + -4x + -8 + 4x

Combine like terms: 24x + 4x = 28x
-8 + 28x + -10x2 = 8 + -4x + -8 + 4x

Reorder the terms:
-8 + 28x + -10x2 = 8 + -8 + -4x + 4x

Combine like terms: 8 + -8 = 0
-8 + 28x + -10x2 = 0 + -4x + 4x
-8 + 28x + -10x2 = -4x + 4x

Combine like terms: -4x + 4x = 0
-8 + 28x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + 14x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + 14x + -5x2)' equal to zero and attempt to solve:

Simplifying
-4 + 14x + -5x2 = 0

Solving
-4 + 14x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
0.8 + -2.8x + x2 = 0

Move the constant term to the right:

Add '-0.8' to each side of the equation.
0.8 + -2.8x + -0.8 + x2 = 0 + -0.8

Reorder the terms:
0.8 + -0.8 + -2.8x + x2 = 0 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + -2.8x + x2 = 0 + -0.8
-2.8x + x2 = 0 + -0.8

Combine like terms: 0 + -0.8 = -0.8
-2.8x + x2 = -0.8

The x term is -2.8x.  Take half its coefficient (-1.4).
Square it (1.96) and add it to both sides.

Add '1.96' to each side of the equation.
-2.8x + 1.96 + x2 = -0.8 + 1.96

Reorder the terms:
1.96 + -2.8x + x2 = -0.8 + 1.96

Combine like terms: -0.8 + 1.96 = 1.16
1.96 + -2.8x + x2 = 1.16

Factor a perfect square on the left side:
(x + -1.4)(x + -1.4) = 1.16

Calculate the square root of the right side: 1.077032961

Break this problem into two subproblems by setting 
(x + -1.4) equal to 1.077032961 and -1.077032961.

Subproblem 1
x + -1.4 = 1.077032961

Simplifying
x + -1.4 = 1.077032961

Reorder the terms:
-1.4 + x = 1.077032961

Solving
-1.4 + x = 1.077032961

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = 1.077032961 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = 1.077032961 + 1.4
x = 1.077032961 + 1.4

Combine like terms: 1.077032961 + 1.4 = 2.477032961
x = 2.477032961

Simplifying
x = 2.477032961

Subproblem 2
x + -1.4 = -1.077032961

Simplifying
x + -1.4 = -1.077032961

Reorder the terms:
-1.4 + x = -1.077032961

Solving
-1.4 + x = -1.077032961

Solving for variable 'x'.

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

Add '1.4' to each side of the equation.
-1.4 + 1.4 + x = -1.077032961 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + x = -1.077032961 + 1.4
x = -1.077032961 + 1.4

Combine like terms: -1.077032961 + 1.4 = 0.322967039
x = 0.322967039

Simplifying
x = 0.322967039

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.477032961, 0.322967039}
Solution
x = {2.477032961, 0.322967039}