(x-8)(4x-8)=160

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Solution for (x-8)(4x-8)=160 equation: 


Simplifying
(x + -8)(4x + -8) = 160

Reorder the terms:
(-8 + x)(4x + -8) = 160

Reorder the terms:
(-8 + x)(-8 + 4x) = 160

Multiply (-8 + x) * (-8 + 4x)
(-8(-8 + 4x) + x(-8 + 4x)) = 160
((-8 * -8 + 4x * -8) + x(-8 + 4x)) = 160
((64 + -32x) + x(-8 + 4x)) = 160
(64 + -32x + (-8 * x + 4x * x)) = 160
(64 + -32x + (-8x + 4x2)) = 160

Combine like terms: -32x + -8x = -40x
(64 + -40x + 4x2) = 160

Solving
64 + -40x + 4x2 = 160

Solving for variable 'x'.

Reorder the terms:
64 + -160 + -40x + 4x2 = 160 + -160

Combine like terms: 64 + -160 = -96
-96 + -40x + 4x2 = 160 + -160

Combine like terms: 160 + -160 = 0
-96 + -40x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-24 + -10x + x2) = 0

Factor a trinomial.
4((-2 + -1x)(12 + -1x)) = 0

Ignore the factor 4.

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 '(12 + -1x)' equal to zero and attempt to solve:

Simplifying
12 + -1x = 0

Solving
12 + -1x = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1x = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1x = 0 + -12
-1x = 0 + -12

Combine like terms: 0 + -12 = -12
-1x = -12

Divide each side by '-1'.
x = 12

Simplifying
x = 12
Solution
x = {-2, 12}

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