(x+3)*(x-4)=120

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Solution for (x+3)*(x-4)=120 equation: 


Simplifying
(x + 3)(x + -4) = 120

Reorder the terms:
(3 + x)(x + -4) = 120

Reorder the terms:
(3 + x)(-4 + x) = 120

Multiply (3 + x) * (-4 + x)
(3(-4 + x) + x(-4 + x)) = 120
((-4 * 3 + x * 3) + x(-4 + x)) = 120
((-12 + 3x) + x(-4 + x)) = 120
(-12 + 3x + (-4 * x + x * x)) = 120
(-12 + 3x + (-4x + x2)) = 120

Combine like terms: 3x + -4x = -1x
(-12 + -1x + x2) = 120

Solving
-12 + -1x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
-12 + -120 + -1x + x2 = 120 + -120

Combine like terms: -12 + -120 = -132
-132 + -1x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-132 + -1x + x2 = 0

Factor a trinomial.
(-11 + -1x)(12 + -1x) = 0


Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11

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 = {-11, 12}

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