5(3x-15)=15x(x-15)

Solution for 5(3x-15)=15x(x-15) equation:

Simplifying
5(3x + -15) = 15x(x + -15)

Reorder the terms:
5(-15 + 3x) = 15x(x + -15)
(-15 * 5 + 3x * 5) = 15x(x + -15)
(-75 + 15x) = 15x(x + -15)

Reorder the terms:
-75 + 15x = 15x(-15 + x)
-75 + 15x = (-15 * 15x + x * 15x)
-75 + 15x = (-225x + 15x2)

Solving
-75 + 15x = -225x + 15x2

Solving for variable 'x'.

Combine like terms: 15x + 225x = 240x
-75 + 240x + -15x2 = -225x + 15x2 + 225x + -15x2

Reorder the terms:
-75 + 240x + -15x2 = -225x + 225x + 15x2 + -15x2

Combine like terms: -225x + 225x = 0
-75 + 240x + -15x2 = 0 + 15x2 + -15x2
-75 + 240x + -15x2 = 15x2 + -15x2

Combine like terms: 15x2 + -15x2 = 0
-75 + 240x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(-5 + 16x + -1x2) = 0

Ignore the factor 15.
Subproblem 1
Set the factor '(-5 + 16x + -1x2)' equal to zero and attempt to solve:

Simplifying
-5 + 16x + -1x2 = 0

Solving
-5 + 16x + -1x2 = 0

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

Divide each side by '-1'.
5 + -16x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -16x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -16x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -16x + x2 = 0 + -5
-16x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-16x + x2 = -5

The x term is -16x.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16x + 64 + x2 = -5 + 64

Reorder the terms:
64 + -16x + x2 = -5 + 64

Combine like terms: -5 + 64 = 59
64 + -16x + x2 = 59

Factor a perfect square on the left side:
(x + -8)(x + -8) = 59

Calculate the square root of the right side: 7.681145748

Break this problem into two subproblems by setting 
(x + -8) equal to 7.681145748 and -7.681145748.

Subproblem 1
x + -8 = 7.681145748

Simplifying
x + -8 = 7.681145748

Reorder the terms:
-8 + x = 7.681145748

Solving
-8 + x = 7.681145748

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = 7.681145748 + 8

Combine like terms: -8 + 8 = 0
0 + x = 7.681145748 + 8
x = 7.681145748 + 8

Combine like terms: 7.681145748 + 8 = 15.681145748
x = 15.681145748

Simplifying
x = 15.681145748

Subproblem 2
x + -8 = -7.681145748

Simplifying
x + -8 = -7.681145748

Reorder the terms:
-8 + x = -7.681145748

Solving
-8 + x = -7.681145748

Solving for variable 'x'.

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

Add '8' to each side of the equation.
-8 + 8 + x = -7.681145748 + 8

Combine like terms: -8 + 8 = 0
0 + x = -7.681145748 + 8
x = -7.681145748 + 8

Combine like terms: -7.681145748 + 8 = 0.318854252
x = 0.318854252

Simplifying
x = 0.318854252

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.681145748, 0.318854252}
Solution
x = {15.681145748, 0.318854252}