180=(x+5)(x+8)

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


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

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

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

Multiply (5 + x) * (8 + x)
180 = (5(8 + x) + x(8 + x))
180 = ((8 * 5 + x * 5) + x(8 + x))
180 = ((40 + 5x) + x(8 + x))
180 = (40 + 5x + (8 * x + x * x))
180 = (40 + 5x + (8x + x2))

Combine like terms: 5x + 8x = 13x
180 = (40 + 13x + x2)

Solving
180 = 40 + 13x + x2

Solving for variable 'x'.

Combine like terms: 180 + -40 = 140
140 + -13x + -1x2 = 40 + 13x + x2 + -40 + -13x + -1x2

Reorder the terms:
140 + -13x + -1x2 = 40 + -40 + 13x + -13x + x2 + -1x2

Combine like terms: 40 + -40 = 0
140 + -13x + -1x2 = 0 + 13x + -13x + x2 + -1x2
140 + -13x + -1x2 = 13x + -13x + x2 + -1x2

Combine like terms: 13x + -13x = 0
140 + -13x + -1x2 = 0 + x2 + -1x2
140 + -13x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
140 + -13x + -1x2 = 0

Factor a trinomial.
(7 + -1x)(20 + x) = 0


Subproblem 1
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7

Subproblem 2
Set the factor '(20 + x)' equal to zero and attempt to solve:

Simplifying
20 + x = 0

Solving
20 + x = 0

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

Add '-20' to each side of the equation.
20 + -20 + x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + x = 0 + -20
x = 0 + -20

Combine like terms: 0 + -20 = -20
x = -20

Simplifying
x = -20
Solution
x = {7, -20}

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