12(4x-4)+8(x-1)=7(4x-4)(x-1)

Solution for 12(4x-4)+8(x-1)=7(4x-4)(x-1) equation:

Simplifying
12(4x + -4) + 8(x + -1) = 7(4x + -4)(x + -1)

Reorder the terms:
12(-4 + 4x) + 8(x + -1) = 7(4x + -4)(x + -1)
(-4 * 12 + 4x * 12) + 8(x + -1) = 7(4x + -4)(x + -1)
(-48 + 48x) + 8(x + -1) = 7(4x + -4)(x + -1)

Reorder the terms:
-48 + 48x + 8(-1 + x) = 7(4x + -4)(x + -1)
-48 + 48x + (-1 * 8 + x * 8) = 7(4x + -4)(x + -1)
-48 + 48x + (-8 + 8x) = 7(4x + -4)(x + -1)

Reorder the terms:
-48 + -8 + 48x + 8x = 7(4x + -4)(x + -1)

Combine like terms: -48 + -8 = -56
-56 + 48x + 8x = 7(4x + -4)(x + -1)

Combine like terms: 48x + 8x = 56x
-56 + 56x = 7(4x + -4)(x + -1)

Reorder the terms:
-56 + 56x = 7(-4 + 4x)(x + -1)

Reorder the terms:
-56 + 56x = 7(-4 + 4x)(-1 + x)

Multiply (-4 + 4x) * (-1 + x)
-56 + 56x = 7(-4(-1 + x) + 4x * (-1 + x))
-56 + 56x = 7((-1 * -4 + x * -4) + 4x * (-1 + x))
-56 + 56x = 7((4 + -4x) + 4x * (-1 + x))
-56 + 56x = 7(4 + -4x + (-1 * 4x + x * 4x))
-56 + 56x = 7(4 + -4x + (-4x + 4x2))

Combine like terms: -4x + -4x = -8x
-56 + 56x = 7(4 + -8x + 4x2)
-56 + 56x = (4 * 7 + -8x * 7 + 4x2 * 7)
-56 + 56x = (28 + -56x + 28x2)

Solving
-56 + 56x = 28 + -56x + 28x2

Solving for variable 'x'.

Reorder the terms:
-56 + -28 + 56x + 56x + -28x2 = 28 + -56x + 28x2 + -28 + 56x + -28x2

Combine like terms: -56 + -28 = -84
-84 + 56x + 56x + -28x2 = 28 + -56x + 28x2 + -28 + 56x + -28x2

Combine like terms: 56x + 56x = 112x
-84 + 112x + -28x2 = 28 + -56x + 28x2 + -28 + 56x + -28x2

Reorder the terms:
-84 + 112x + -28x2 = 28 + -28 + -56x + 56x + 28x2 + -28x2

Combine like terms: 28 + -28 = 0
-84 + 112x + -28x2 = 0 + -56x + 56x + 28x2 + -28x2
-84 + 112x + -28x2 = -56x + 56x + 28x2 + -28x2

Combine like terms: -56x + 56x = 0
-84 + 112x + -28x2 = 0 + 28x2 + -28x2
-84 + 112x + -28x2 = 28x2 + -28x2

Combine like terms: 28x2 + -28x2 = 0
-84 + 112x + -28x2 = 0

Factor out the Greatest Common Factor (GCF), '28'.
28(-3 + 4x + -1x2) = 0

Factor a trinomial.
28((-3 + x)(1 + -1x)) = 0

Ignore the factor 28.
Subproblem 1
Set the factor '(-3 + x)' equal to zero and attempt to solve:

Simplifying
-3 + x = 0

Solving
-3 + x = 0

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

Add '3' to each side of the equation.
-3 + 3 + x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + x = 0 + 3
x = 0 + 3

Combine like terms: 0 + 3 = 3
x = 3

Simplifying
x = 3
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {3, 1}