(x+9)(x-6)=0

Solution for (x+9)(x-6)=0 equation:

Simplifying
(x + 9)(x + -6) = 0

Reorder the terms:
(9 + x)(x + -6) = 0

Reorder the terms:
(9 + x)(-6 + x) = 0

Multiply (9 + x) * (-6 + x)
(9(-6 + x) + x(-6 + x)) = 0
((-6 * 9 + x * 9) + x(-6 + x)) = 0
((-54 + 9x) + x(-6 + x)) = 0
(-54 + 9x + (-6 * x + x * x)) = 0
(-54 + 9x + (-6x + x2)) = 0

Combine like terms: 9x + -6x = 3x
(-54 + 3x + x2) = 0

Solving
-54 + 3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-9 + -1x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
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 = {-9, 6}