(x+6)(x+8)=120

Solution for (x+6)(x+8)=120 equation:

Simplifying
(x + 6)(x + 8) = 120

Reorder the terms:
(6 + x)(x + 8) = 120

Reorder the terms:
(6 + x)(8 + x) = 120

Multiply (6 + x) * (8 + x)
(6(8 + x) + x(8 + x)) = 120
((8 * 6 + x * 6) + x(8 + x)) = 120
((48 + 6x) + x(8 + x)) = 120
(48 + 6x + (8 * x + x * x)) = 120
(48 + 6x + (8x + x2)) = 120

Combine like terms: 6x + 8x = 14x
(48 + 14x + x2) = 120

Solving
48 + 14x + x2 = 120

Solving for variable 'x'.

Reorder the terms:
48 + -120 + 14x + x2 = 120 + -120

Combine like terms: 48 + -120 = -72
-72 + 14x + x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-72 + 14x + x2 = 0

Factor a trinomial.
(-18 + -1x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-18, 4}