-5x(2x-2)=10(-9x-9)

Solution for -5x(2x-2)=10(-9x-9) equation:

Simplifying
-5x(2x + -2) = 10(-9x + -9)

Reorder the terms:
-5x(-2 + 2x) = 10(-9x + -9)
(-2 * -5x + 2x * -5x) = 10(-9x + -9)
(10x + -10x2) = 10(-9x + -9)

Reorder the terms:
10x + -10x2 = 10(-9 + -9x)
10x + -10x2 = (-9 * 10 + -9x * 10)
10x + -10x2 = (-90 + -90x)

Solving
10x + -10x2 = -90 + -90x

Solving for variable 'x'.

Reorder the terms:
90 + 10x + 90x + -10x2 = -90 + -90x + 90 + 90x

Combine like terms: 10x + 90x = 100x
90 + 100x + -10x2 = -90 + -90x + 90 + 90x

Reorder the terms:
90 + 100x + -10x2 = -90 + 90 + -90x + 90x

Combine like terms: -90 + 90 = 0
90 + 100x + -10x2 = 0 + -90x + 90x
90 + 100x + -10x2 = -90x + 90x

Combine like terms: -90x + 90x = 0
90 + 100x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(9 + 10x + -1x2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(9 + 10x + -1x2)' equal to zero and attempt to solve:

Simplifying
9 + 10x + -1x2 = 0

Solving
9 + 10x + -1x2 = 0

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

Divide each side by '-1'.
-9 + -10x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -10x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -10x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -10x + x2 = 0 + 9
-10x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-10x + x2 = 9

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 9 + 25

Reorder the terms:
25 + -10x + x2 = 9 + 25

Combine like terms: 9 + 25 = 34
25 + -10x + x2 = 34

Factor a perfect square on the left side:
(x + -5)(x + -5) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -5) equal to 5.830951895 and -5.830951895.

Subproblem 1
x + -5 = 5.830951895

Simplifying
x + -5 = 5.830951895

Reorder the terms:
-5 + x = 5.830951895

Solving
-5 + x = 5.830951895

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.830951895 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.830951895 + 5
x = 5.830951895 + 5

Combine like terms: 5.830951895 + 5 = 10.830951895
x = 10.830951895

Simplifying
x = 10.830951895

Subproblem 2
x + -5 = -5.830951895

Simplifying
x + -5 = -5.830951895

Reorder the terms:
-5 + x = -5.830951895

Solving
-5 + x = -5.830951895

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.830951895 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.830951895 + 5
x = -5.830951895 + 5

Combine like terms: -5.830951895 + 5 = -0.830951895
x = -0.830951895

Simplifying
x = -0.830951895

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.830951895, -0.830951895}
Solution
x = {10.830951895, -0.830951895}