(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 = -15x
(54 + -15x + x2) = 0

Solving
54 + -15x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {6, 9}