x(6x-4)=(6x+8)(6x-6)

Solution for x(6x-4)=(6x+8)(6x-6) equation:

Simplifying
x(6x + -4) = (6x + 8)(6x + -6)

Reorder the terms:
x(-4 + 6x) = (6x + 8)(6x + -6)
(-4 * x + 6x * x) = (6x + 8)(6x + -6)
(-4x + 6x2) = (6x + 8)(6x + -6)

Reorder the terms:
-4x + 6x2 = (8 + 6x)(6x + -6)

Reorder the terms:
-4x + 6x2 = (8 + 6x)(-6 + 6x)

Multiply (8 + 6x) * (-6 + 6x)
-4x + 6x2 = (8(-6 + 6x) + 6x * (-6 + 6x))
-4x + 6x2 = ((-6 * 8 + 6x * 8) + 6x * (-6 + 6x))
-4x + 6x2 = ((-48 + 48x) + 6x * (-6 + 6x))
-4x + 6x2 = (-48 + 48x + (-6 * 6x + 6x * 6x))
-4x + 6x2 = (-48 + 48x + (-36x + 36x2))

Combine like terms: 48x + -36x = 12x
-4x + 6x2 = (-48 + 12x + 36x2)

Solving
-4x + 6x2 = -48 + 12x + 36x2

Solving for variable 'x'.

Reorder the terms:
48 + -4x + -12x + 6x2 + -36x2 = -48 + 12x + 36x2 + 48 + -12x + -36x2

Combine like terms: -4x + -12x = -16x
48 + -16x + 6x2 + -36x2 = -48 + 12x + 36x2 + 48 + -12x + -36x2

Combine like terms: 6x2 + -36x2 = -30x2
48 + -16x + -30x2 = -48 + 12x + 36x2 + 48 + -12x + -36x2

Reorder the terms:
48 + -16x + -30x2 = -48 + 48 + 12x + -12x + 36x2 + -36x2

Combine like terms: -48 + 48 = 0
48 + -16x + -30x2 = 0 + 12x + -12x + 36x2 + -36x2
48 + -16x + -30x2 = 12x + -12x + 36x2 + -36x2

Combine like terms: 12x + -12x = 0
48 + -16x + -30x2 = 0 + 36x2 + -36x2
48 + -16x + -30x2 = 36x2 + -36x2

Combine like terms: 36x2 + -36x2 = 0
48 + -16x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -8x + -15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(24 + -8x + -15x2)' equal to zero and attempt to solve:

Simplifying
24 + -8x + -15x2 = 0

Solving
24 + -8x + -15x2 = 0

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
-1.6 + 0.5333333333x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 0.5333333333x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 0.5333333333x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 0.5333333333x + x2 = 0 + 1.6
0.5333333333x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
0.5333333333x + x2 = 1.6

The x term is 0.5333333333x.  Take half its coefficient (0.2666666667).
Square it (0.07111111113) and add it to both sides.

Add '0.07111111113' to each side of the equation.
0.5333333333x + 0.07111111113 + x2 = 1.6 + 0.07111111113

Reorder the terms:
0.07111111113 + 0.5333333333x + x2 = 1.6 + 0.07111111113

Combine like terms: 1.6 + 0.07111111113 = 1.67111111113
0.07111111113 + 0.5333333333x + x2 = 1.67111111113

Factor a perfect square on the left side:
(x + 0.2666666667)(x + 0.2666666667) = 1.67111111113

Calculate the square root of the right side: 1.292714629

Break this problem into two subproblems by setting 
(x + 0.2666666667) equal to 1.292714629 and -1.292714629.

Subproblem 1
x + 0.2666666667 = 1.292714629

Simplifying
x + 0.2666666667 = 1.292714629

Reorder the terms:
0.2666666667 + x = 1.292714629

Solving
0.2666666667 + x = 1.292714629

Solving for variable 'x'.

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

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -0.2666666667 + x = 1.292714629 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + x = 1.292714629 + -0.2666666667
x = 1.292714629 + -0.2666666667

Combine like terms: 1.292714629 + -0.2666666667 = 1.0260479623
x = 1.0260479623

Simplifying
x = 1.0260479623

Subproblem 2
x + 0.2666666667 = -1.292714629

Simplifying
x + 0.2666666667 = -1.292714629

Reorder the terms:
0.2666666667 + x = -1.292714629

Solving
0.2666666667 + x = -1.292714629

Solving for variable 'x'.

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

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -0.2666666667 + x = -1.292714629 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + x = -1.292714629 + -0.2666666667
x = -1.292714629 + -0.2666666667

Combine like terms: -1.292714629 + -0.2666666667 = -1.5593812957
x = -1.5593812957

Simplifying
x = -1.5593812957

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.0260479623, -1.5593812957}
Solution
x = {1.0260479623, -1.5593812957}