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

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

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

Reorder the terms:
4(-5 + x) + 2(x) = -5(x)(x + -5)
(-5 * 4 + x * 4) + 2(x) = -5(x)(x + -5)
(-20 + 4x) + 2(x) = -5(x)(x + -5)

Combine like terms: 4x + 2x = 6x
-20 + 6x = -5(x)(x + -5)

Reorder the terms:
-20 + 6x = -5x(-5 + x)
-20 + 6x = (-5 * -5x + x * -5x)
-20 + 6x = (25x + -5x2)

Solving
-20 + 6x = 25x + -5x2

Solving for variable 'x'.

Combine like terms: 6x + -25x = -19x
-20 + -19x + 5x2 = 25x + -5x2 + -25x + 5x2

Reorder the terms:
-20 + -19x + 5x2 = 25x + -25x + -5x2 + 5x2

Combine like terms: 25x + -25x = 0
-20 + -19x + 5x2 = 0 + -5x2 + 5x2
-20 + -19x + 5x2 = -5x2 + 5x2

Combine like terms: -5x2 + 5x2 = 0
-20 + -19x + 5x2 = 0

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

Divide each side by '5'.
-4 + -3.8x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -3.8x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -3.8x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3.8x + x2 = 0 + 4
-3.8x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-3.8x + x2 = 4

The x term is -3.8x.  Take half its coefficient (-1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
-3.8x + 3.61 + x2 = 4 + 3.61

Reorder the terms:
3.61 + -3.8x + x2 = 4 + 3.61

Combine like terms: 4 + 3.61 = 7.61
3.61 + -3.8x + x2 = 7.61

Factor a perfect square on the left side:
(x + -1.9)(x + -1.9) = 7.61

Calculate the square root of the right side: 2.758622845

Break this problem into two subproblems by setting 
(x + -1.9) equal to 2.758622845 and -2.758622845.

Subproblem 1
x + -1.9 = 2.758622845

Simplifying
x + -1.9 = 2.758622845

Reorder the terms:
-1.9 + x = 2.758622845

Solving
-1.9 + x = 2.758622845

Solving for variable 'x'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + x = 2.758622845 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + x = 2.758622845 + 1.9
x = 2.758622845 + 1.9

Combine like terms: 2.758622845 + 1.9 = 4.658622845
x = 4.658622845

Simplifying
x = 4.658622845

Subproblem 2
x + -1.9 = -2.758622845

Simplifying
x + -1.9 = -2.758622845

Reorder the terms:
-1.9 + x = -2.758622845

Solving
-1.9 + x = -2.758622845

Solving for variable 'x'.

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

Add '1.9' to each side of the equation.
-1.9 + 1.9 + x = -2.758622845 + 1.9

Combine like terms: -1.9 + 1.9 = 0.0
0.0 + x = -2.758622845 + 1.9
x = -2.758622845 + 1.9

Combine like terms: -2.758622845 + 1.9 = -0.858622845
x = -0.858622845

Simplifying
x = -0.858622845

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.658622845, -0.858622845}