(x+9)(x+6)=108

Solution for (x+9)(x+6)=108 equation:

Simplifying
(x + 9)(x + 6) = 108

Reorder the terms:
(9 + x)(x + 6) = 108

Reorder the terms:
(9 + x)(6 + x) = 108

Multiply (9 + x) * (6 + x)
(9(6 + x) + x(6 + x)) = 108
((6 * 9 + x * 9) + x(6 + x)) = 108
((54 + 9x) + x(6 + x)) = 108
(54 + 9x + (6 * x + x * x)) = 108
(54 + 9x + (6x + x2)) = 108

Combine like terms: 9x + 6x = 15x
(54 + 15x + x2) = 108

Solving
54 + 15x + x2 = 108

Solving for variable 'x'.

Reorder the terms:
54 + -108 + 15x + x2 = 108 + -108

Combine like terms: 54 + -108 = -54
-54 + 15x + x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-54 + 15x + x2 = 0

Factor a trinomial.
(-18 + -1x)(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-18, 3}