-10x(x-5)=-8(x+9)

Solution for -10x(x-5)=-8(x+9) equation:

Simplifying
-10x(x + -5) = -8(x + 9)

Reorder the terms:
-10x(-5 + x) = -8(x + 9)
(-5 * -10x + x * -10x) = -8(x + 9)
(50x + -10x2) = -8(x + 9)

Reorder the terms:
50x + -10x2 = -8(9 + x)
50x + -10x2 = (9 * -8 + x * -8)
50x + -10x2 = (-72 + -8x)

Solving
50x + -10x2 = -72 + -8x

Solving for variable 'x'.

Reorder the terms:
72 + 50x + 8x + -10x2 = -72 + -8x + 72 + 8x

Combine like terms: 50x + 8x = 58x
72 + 58x + -10x2 = -72 + -8x + 72 + 8x

Reorder the terms:
72 + 58x + -10x2 = -72 + 72 + -8x + 8x

Combine like terms: -72 + 72 = 0
72 + 58x + -10x2 = 0 + -8x + 8x
72 + 58x + -10x2 = -8x + 8x

Combine like terms: -8x + 8x = 0
72 + 58x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(36 + 29x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(36 + 29x + -5x2)' equal to zero and attempt to solve:

Simplifying
36 + 29x + -5x2 = 0

Solving
36 + 29x + -5x2 = 0

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

Divide each side by '-5'.
-7.2 + -5.8x + x2 = 0

Move the constant term to the right:

Add '7.2' to each side of the equation.
-7.2 + -5.8x + 7.2 + x2 = 0 + 7.2

Reorder the terms:
-7.2 + 7.2 + -5.8x + x2 = 0 + 7.2

Combine like terms: -7.2 + 7.2 = 0.0
0.0 + -5.8x + x2 = 0 + 7.2
-5.8x + x2 = 0 + 7.2

Combine like terms: 0 + 7.2 = 7.2
-5.8x + x2 = 7.2

The x term is -5.8x.  Take half its coefficient (-2.9).
Square it (8.41) and add it to both sides.

Add '8.41' to each side of the equation.
-5.8x + 8.41 + x2 = 7.2 + 8.41

Reorder the terms:
8.41 + -5.8x + x2 = 7.2 + 8.41

Combine like terms: 7.2 + 8.41 = 15.61
8.41 + -5.8x + x2 = 15.61

Factor a perfect square on the left side:
(x + -2.9)(x + -2.9) = 15.61

Calculate the square root of the right side: 3.950949253

Break this problem into two subproblems by setting 
(x + -2.9) equal to 3.950949253 and -3.950949253.

Subproblem 1
x + -2.9 = 3.950949253

Simplifying
x + -2.9 = 3.950949253

Reorder the terms:
-2.9 + x = 3.950949253

Solving
-2.9 + x = 3.950949253

Solving for variable 'x'.

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

Add '2.9' to each side of the equation.
-2.9 + 2.9 + x = 3.950949253 + 2.9

Combine like terms: -2.9 + 2.9 = 0.0
0.0 + x = 3.950949253 + 2.9
x = 3.950949253 + 2.9

Combine like terms: 3.950949253 + 2.9 = 6.850949253
x = 6.850949253

Simplifying
x = 6.850949253

Subproblem 2
x + -2.9 = -3.950949253

Simplifying
x + -2.9 = -3.950949253

Reorder the terms:
-2.9 + x = -3.950949253

Solving
-2.9 + x = -3.950949253

Solving for variable 'x'.

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

Add '2.9' to each side of the equation.
-2.9 + 2.9 + x = -3.950949253 + 2.9

Combine like terms: -2.9 + 2.9 = 0.0
0.0 + x = -3.950949253 + 2.9
x = -3.950949253 + 2.9

Combine like terms: -3.950949253 + 2.9 = -1.050949253
x = -1.050949253

Simplifying
x = -1.050949253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.850949253, -1.050949253}
Solution
x = {6.850949253, -1.050949253}