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

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

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

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

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

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

Combine like terms: -6x + 9x = 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}