32-4x=(2x+2)(x-4)

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Solution for 32-4x=(2x+2)(x-4) equation: 


Simplifying
32 + -4x = (2x + 2)(x + -4)

Reorder the terms:
32 + -4x = (2 + 2x)(x + -4)

Reorder the terms:
32 + -4x = (2 + 2x)(-4 + x)

Multiply (2 + 2x) * (-4 + x)
32 + -4x = (2(-4 + x) + 2x * (-4 + x))
32 + -4x = ((-4 * 2 + x * 2) + 2x * (-4 + x))
32 + -4x = ((-8 + 2x) + 2x * (-4 + x))
32 + -4x = (-8 + 2x + (-4 * 2x + x * 2x))
32 + -4x = (-8 + 2x + (-8x + 2x2))

Combine like terms: 2x + -8x = -6x
32 + -4x = (-8 + -6x + 2x2)

Solving
32 + -4x = -8 + -6x + 2x2

Solving for variable 'x'.

Reorder the terms:
32 + 8 + -4x + 6x + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: 32 + 8 = 40
40 + -4x + 6x + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Combine like terms: -4x + 6x = 2x
40 + 2x + -2x2 = -8 + -6x + 2x2 + 8 + 6x + -2x2

Reorder the terms:
40 + 2x + -2x2 = -8 + 8 + -6x + 6x + 2x2 + -2x2

Combine like terms: -8 + 8 = 0
40 + 2x + -2x2 = 0 + -6x + 6x + 2x2 + -2x2
40 + 2x + -2x2 = -6x + 6x + 2x2 + -2x2

Combine like terms: -6x + 6x = 0
40 + 2x + -2x2 = 0 + 2x2 + -2x2
40 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
40 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + x + -1x2) = 0

Factor a trinomial.
2((5 + -1x)(4 + x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Solution
x = {5, -4}

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