-5x(x-15)=-10x+20

Solution for -5x(x-15)=-10x+20 equation:

Simplifying
-5x(x + -15) = -10x + 20

Reorder the terms:
-5x(-15 + x) = -10x + 20
(-15 * -5x + x * -5x) = -10x + 20
(75x + -5x2) = -10x + 20

Reorder the terms:
75x + -5x2 = 20 + -10x

Solving
75x + -5x2 = 20 + -10x

Solving for variable 'x'.

Reorder the terms:
-20 + 75x + 10x + -5x2 = 20 + -10x + -20 + 10x

Combine like terms: 75x + 10x = 85x
-20 + 85x + -5x2 = 20 + -10x + -20 + 10x

Reorder the terms:
-20 + 85x + -5x2 = 20 + -20 + -10x + 10x

Combine like terms: 20 + -20 = 0
-20 + 85x + -5x2 = 0 + -10x + 10x
-20 + 85x + -5x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-20 + 85x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 17x + -1x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-4 + 17x + -1x2)' equal to zero and attempt to solve:

Simplifying
-4 + 17x + -1x2 = 0

Solving
-4 + 17x + -1x2 = 0

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

Divide each side by '-1'.
4 + -17x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -17x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -17x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -17x + x2 = 0 + -4
-17x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-17x + x2 = -4

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = -4 + 72.25

Reorder the terms:
72.25 + -17x + x2 = -4 + 72.25

Combine like terms: -4 + 72.25 = 68.25
72.25 + -17x + x2 = 68.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 68.25

Calculate the square root of the right side: 8.261355821

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.261355821 and -8.261355821.

Subproblem 1
x + -8.5 = 8.261355821

Simplifying
x + -8.5 = 8.261355821

Reorder the terms:
-8.5 + x = 8.261355821

Solving
-8.5 + x = 8.261355821

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = 8.261355821 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = 8.261355821 + 8.5
x = 8.261355821 + 8.5

Combine like terms: 8.261355821 + 8.5 = 16.761355821
x = 16.761355821

Simplifying
x = 16.761355821

Subproblem 2
x + -8.5 = -8.261355821

Simplifying
x + -8.5 = -8.261355821

Reorder the terms:
-8.5 + x = -8.261355821

Solving
-8.5 + x = -8.261355821

Solving for variable 'x'.

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

Add '8.5' to each side of the equation.
-8.5 + 8.5 + x = -8.261355821 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + x = -8.261355821 + 8.5
x = -8.261355821 + 8.5

Combine like terms: -8.261355821 + 8.5 = 0.238644179
x = 0.238644179

Simplifying
x = 0.238644179

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.761355821, 0.238644179}
Solution
x = {16.761355821, 0.238644179}