(x+9)(x-5)-15=0

Solution for (x+9)(x-5)-15=0 equation:

Simplifying
(x + 9)(x + -5) + -15 = 0

Reorder the terms:
(9 + x)(x + -5) + -15 = 0

Reorder the terms:
(9 + x)(-5 + x) + -15 = 0

Multiply (9 + x) * (-5 + x)
(9(-5 + x) + x(-5 + x)) + -15 = 0
((-5 * 9 + x * 9) + x(-5 + x)) + -15 = 0
((-45 + 9x) + x(-5 + x)) + -15 = 0
(-45 + 9x + (-5 * x + x * x)) + -15 = 0
(-45 + 9x + (-5x + x2)) + -15 = 0

Combine like terms: 9x + -5x = 4x
(-45 + 4x + x2) + -15 = 0

Reorder the terms:
-45 + -15 + 4x + x2 = 0

Combine like terms: -45 + -15 = -60
-60 + 4x + x2 = 0

Solving
-60 + 4x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -1x)(6 + -1x) = 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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-10, 6}