(x+2)(x+4)=120

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Solution for (x+2)(x+4)=120 equation:


Simplifying
(x + 2)(x + 4) = 120

Reorder the terms:
(2 + x)(x + 4) = 120

Reorder the terms:
(2 + x)(4 + x) = 120

Multiply (2 + x) * (4 + x)
(2(4 + x) + x(4 + x)) = 120
((4 * 2 + x * 2) + x(4 + x)) = 120
((8 + 2x) + x(4 + x)) = 120
(8 + 2x + (4 * x + x * x)) = 120
(8 + 2x + (4x + x2)) = 120

Combine like terms: 2x + 4x = 6x
(8 + 6x + x2) = 120

Solving
8 + 6x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
8 + -120 + 6x + x2 = 120 + -120

Combine like terms: 8 + -120 = -112
-112 + 6x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-112 + 6x + x2 = 0

Factor a trinomial.
(-14 + -1x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-14 + -1x)' equal to zero and attempt to solve: Simplifying -14 + -1x = 0 Solving -14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + -1x = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x = 0 + 14 -1x = 0 + 14 Combine like terms: 0 + 14 = 14 -1x = 14 Divide each side by '-1'. x = -14 Simplifying x = -14

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-14, 8}

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