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

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


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

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

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

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

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

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

Multiply (2 + x) * (1 + -2x)
32 + -28x + 3x2 = (2(1 + -2x) + x(1 + -2x))
32 + -28x + 3x2 = ((1 * 2 + -2x * 2) + x(1 + -2x))
32 + -28x + 3x2 = ((2 + -4x) + x(1 + -2x))
32 + -28x + 3x2 = (2 + -4x + (1 * x + -2x * x))
32 + -28x + 3x2 = (2 + -4x + (1x + -2x2))

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

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

Solving for variable 'x'.

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

Combine like terms: 32 + -2 = 30
30 + -28x + 3x + 3x2 + 2x2 = 2 + -3x + -2x2 + -2 + 3x + 2x2

Combine like terms: -28x + 3x = -25x
30 + -25x + 3x2 + 2x2 = 2 + -3x + -2x2 + -2 + 3x + 2x2

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

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

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

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

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

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

Factor a trinomial.
5((2 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {2, 3}

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