180=((3x+5)-8)*(x-8)

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Solution for 180=((3x+5)-8)*(x-8) equation: 


Simplifying
180 = ((3x + 5) + -8)(x + -8)

Reorder the terms:
180 = ((5 + 3x) + -8)(x + -8)

Remove parenthesis around (5 + 3x)
180 = (5 + 3x + -8)(x + -8)

Reorder the terms:
180 = (5 + -8 + 3x)(x + -8)

Combine like terms: 5 + -8 = -3
180 = (-3 + 3x)(x + -8)

Reorder the terms:
180 = (-3 + 3x)(-8 + x)

Multiply (-3 + 3x) * (-8 + x)
180 = (-3(-8 + x) + 3x * (-8 + x))
180 = ((-8 * -3 + x * -3) + 3x * (-8 + x))
180 = ((24 + -3x) + 3x * (-8 + x))
180 = (24 + -3x + (-8 * 3x + x * 3x))
180 = (24 + -3x + (-24x + 3x2))

Combine like terms: -3x + -24x = -27x
180 = (24 + -27x + 3x2)

Solving
180 = 24 + -27x + 3x2

Solving for variable 'x'.

Combine like terms: 180 + -24 = 156
156 + 27x + -3x2 = 24 + -27x + 3x2 + -24 + 27x + -3x2

Reorder the terms:
156 + 27x + -3x2 = 24 + -24 + -27x + 27x + 3x2 + -3x2

Combine like terms: 24 + -24 = 0
156 + 27x + -3x2 = 0 + -27x + 27x + 3x2 + -3x2
156 + 27x + -3x2 = -27x + 27x + 3x2 + -3x2

Combine like terms: -27x + 27x = 0
156 + 27x + -3x2 = 0 + 3x2 + -3x2
156 + 27x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
156 + 27x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(52 + 9x + -1x2) = 0

Factor a trinomial.
3((13 + -1x)(4 + x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13

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 = {13, -4}

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