(x-8)(3x-4)=(1-2x)(x+22)

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Solution for (x-8)(3x-4)=(1-2x)(x+22) equation: 


Simplifying
(x + -8)(3x + -4) = (1 + -2x)(x + 22)

Reorder the terms:
(-8 + x)(3x + -4) = (1 + -2x)(x + 22)

Reorder the terms:
(-8 + x)(-4 + 3x) = (1 + -2x)(x + 22)

Multiply (-8 + x) * (-4 + 3x)
(-8(-4 + 3x) + x(-4 + 3x)) = (1 + -2x)(x + 22)
((-4 * -8 + 3x * -8) + x(-4 + 3x)) = (1 + -2x)(x + 22)
((32 + -24x) + x(-4 + 3x)) = (1 + -2x)(x + 22)
(32 + -24x + (-4 * x + 3x * x)) = (1 + -2x)(x + 22)
(32 + -24x + (-4x + 3x2)) = (1 + -2x)(x + 22)

Combine like terms: -24x + -4x = -28x
(32 + -28x + 3x2) = (1 + -2x)(x + 22)

Reorder the terms:
32 + -28x + 3x2 = (1 + -2x)(22 + x)

Multiply (1 + -2x) * (22 + x)
32 + -28x + 3x2 = (1(22 + x) + -2x * (22 + x))
32 + -28x + 3x2 = ((22 * 1 + x * 1) + -2x * (22 + x))
32 + -28x + 3x2 = ((22 + 1x) + -2x * (22 + x))
32 + -28x + 3x2 = (22 + 1x + (22 * -2x + x * -2x))
32 + -28x + 3x2 = (22 + 1x + (-44x + -2x2))

Combine like terms: 1x + -44x = -43x
32 + -28x + 3x2 = (22 + -43x + -2x2)

Solving
32 + -28x + 3x2 = 22 + -43x + -2x2

Solving for variable 'x'.

Reorder the terms:
32 + -22 + -28x + 43x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: 32 + -22 = 10
10 + -28x + 43x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: -28x + 43x = 15x
10 + 15x + 3x2 + 2x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Combine like terms: 3x2 + 2x2 = 5x2
10 + 15x + 5x2 = 22 + -43x + -2x2 + -22 + 43x + 2x2

Reorder the terms:
10 + 15x + 5x2 = 22 + -22 + -43x + 43x + -2x2 + 2x2

Combine like terms: 22 + -22 = 0
10 + 15x + 5x2 = 0 + -43x + 43x + -2x2 + 2x2
10 + 15x + 5x2 = -43x + 43x + -2x2 + 2x2

Combine like terms: -43x + 43x = 0
10 + 15x + 5x2 = 0 + -2x2 + 2x2
10 + 15x + 5x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
10 + 15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + 3x + x2) = 0

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

Ignore the factor 5.

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

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {-2, -1}

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