(4x-4)(2x-6)=(3x+1)(x-1)

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Solution for (4x-4)(2x-6)=(3x+1)(x-1) equation: 


Simplifying
(4x + -4)(2x + -6) = (3x + 1)(x + -1)

Reorder the terms:
(-4 + 4x)(2x + -6) = (3x + 1)(x + -1)

Reorder the terms:
(-4 + 4x)(-6 + 2x) = (3x + 1)(x + -1)

Multiply (-4 + 4x) * (-6 + 2x)
(-4(-6 + 2x) + 4x * (-6 + 2x)) = (3x + 1)(x + -1)
((-6 * -4 + 2x * -4) + 4x * (-6 + 2x)) = (3x + 1)(x + -1)
((24 + -8x) + 4x * (-6 + 2x)) = (3x + 1)(x + -1)
(24 + -8x + (-6 * 4x + 2x * 4x)) = (3x + 1)(x + -1)
(24 + -8x + (-24x + 8x2)) = (3x + 1)(x + -1)

Combine like terms: -8x + -24x = -32x
(24 + -32x + 8x2) = (3x + 1)(x + -1)

Reorder the terms:
24 + -32x + 8x2 = (1 + 3x)(x + -1)

Reorder the terms:
24 + -32x + 8x2 = (1 + 3x)(-1 + x)

Multiply (1 + 3x) * (-1 + x)
24 + -32x + 8x2 = (1(-1 + x) + 3x * (-1 + x))
24 + -32x + 8x2 = ((-1 * 1 + x * 1) + 3x * (-1 + x))
24 + -32x + 8x2 = ((-1 + 1x) + 3x * (-1 + x))
24 + -32x + 8x2 = (-1 + 1x + (-1 * 3x + x * 3x))
24 + -32x + 8x2 = (-1 + 1x + (-3x + 3x2))

Combine like terms: 1x + -3x = -2x
24 + -32x + 8x2 = (-1 + -2x + 3x2)

Solving
24 + -32x + 8x2 = -1 + -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
24 + 1 + -32x + 2x + 8x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: 24 + 1 = 25
25 + -32x + 2x + 8x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: -32x + 2x = -30x
25 + -30x + 8x2 + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
25 + -30x + 5x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Reorder the terms:
25 + -30x + 5x2 = -1 + 1 + -2x + 2x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
25 + -30x + 5x2 = 0 + -2x + 2x + 3x2 + -3x2
25 + -30x + 5x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
25 + -30x + 5x2 = 0 + 3x2 + -3x2
25 + -30x + 5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
25 + -30x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(5 + -6x + x2) = 0

Factor a trinomial.
5((1 + -1x)(5 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1, 5}

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