120=(x+5)(x-2)

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Solution for 120=(x+5)(x-2) equation: 


Simplifying
120 = (x + 5)(x + -2)

Reorder the terms:
120 = (5 + x)(x + -2)

Reorder the terms:
120 = (5 + x)(-2 + x)

Multiply (5 + x) * (-2 + x)
120 = (5(-2 + x) + x(-2 + x))
120 = ((-2 * 5 + x * 5) + x(-2 + x))
120 = ((-10 + 5x) + x(-2 + x))
120 = (-10 + 5x + (-2 * x + x * x))
120 = (-10 + 5x + (-2x + x2))

Combine like terms: 5x + -2x = 3x
120 = (-10 + 3x + x2)

Solving
120 = -10 + 3x + x2

Solving for variable 'x'.

Combine like terms: 120 + 10 = 130
130 + -3x + -1x2 = -10 + 3x + x2 + 10 + -3x + -1x2

Reorder the terms:
130 + -3x + -1x2 = -10 + 10 + 3x + -3x + x2 + -1x2

Combine like terms: -10 + 10 = 0
130 + -3x + -1x2 = 0 + 3x + -3x + x2 + -1x2
130 + -3x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
130 + -3x + -1x2 = 0 + x2 + -1x2
130 + -3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
130 + -3x + -1x2 = 0

Factor a trinomial.
(10 + -1x)(13 + x) = 0


Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 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 + x = 0 + -13

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

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

Simplifying
x = -13
Solution
x = {10, -13}

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