3(x^2-x)=2(x-4)(x-4)

Solution for 3(x^2-x)=2(x-4)(x-4) equation:

Simplifying
3(x2 + -1x) = 2(x + -4)(x + -4)

Reorder the terms:
3(-1x + x2) = 2(x + -4)(x + -4)
(-1x * 3 + x2 * 3) = 2(x + -4)(x + -4)
(-3x + 3x2) = 2(x + -4)(x + -4)

Reorder the terms:
-3x + 3x2 = 2(-4 + x)(x + -4)

Reorder the terms:
-3x + 3x2 = 2(-4 + x)(-4 + x)

Multiply (-4 + x) * (-4 + x)
-3x + 3x2 = 2(-4(-4 + x) + x(-4 + x))
-3x + 3x2 = 2((-4 * -4 + x * -4) + x(-4 + x))
-3x + 3x2 = 2((16 + -4x) + x(-4 + x))
-3x + 3x2 = 2(16 + -4x + (-4 * x + x * x))
-3x + 3x2 = 2(16 + -4x + (-4x + x2))

Combine like terms: -4x + -4x = -8x
-3x + 3x2 = 2(16 + -8x + x2)
-3x + 3x2 = (16 * 2 + -8x * 2 + x2 * 2)
-3x + 3x2 = (32 + -16x + 2x2)

Solving
-3x + 3x2 = 32 + -16x + 2x2

Solving for variable 'x'.

Reorder the terms:
-32 + -3x + 16x + 3x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: -3x + 16x = 13x
-32 + 13x + 3x2 + -2x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Combine like terms: 3x2 + -2x2 = 1x2
-32 + 13x + 1x2 = 32 + -16x + 2x2 + -32 + 16x + -2x2

Reorder the terms:
-32 + 13x + 1x2 = 32 + -32 + -16x + 16x + 2x2 + -2x2

Combine like terms: 32 + -32 = 0
-32 + 13x + 1x2 = 0 + -16x + 16x + 2x2 + -2x2
-32 + 13x + 1x2 = -16x + 16x + 2x2 + -2x2

Combine like terms: -16x + 16x = 0
-32 + 13x + 1x2 = 0 + 2x2 + -2x2
-32 + 13x + 1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-32 + 13x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + 13x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + 13x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + 13x + x2 = 0 + 32
13x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
13x + x2 = 32

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 32 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 32 + 42.25

Combine like terms: 32 + 42.25 = 74.25
42.25 + 13x + x2 = 74.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + 6.5) equal to 8.61684397 and -8.61684397.

Subproblem 1
x + 6.5 = 8.61684397

Simplifying
x + 6.5 = 8.61684397

Reorder the terms:
6.5 + x = 8.61684397

Solving
6.5 + x = 8.61684397

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 8.61684397 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 8.61684397 + -6.5
x = 8.61684397 + -6.5

Combine like terms: 8.61684397 + -6.5 = 2.11684397
x = 2.11684397

Simplifying
x = 2.11684397

Subproblem 2
x + 6.5 = -8.61684397

Simplifying
x + 6.5 = -8.61684397

Reorder the terms:
6.5 + x = -8.61684397

Solving
6.5 + x = -8.61684397

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -8.61684397 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -8.61684397 + -6.5
x = -8.61684397 + -6.5

Combine like terms: -8.61684397 + -6.5 = -15.11684397
x = -15.11684397

Simplifying
x = -15.11684397

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.11684397, -15.11684397}