(a-9)(a-6)=0

Solution for (a-9)(a-6)=0 equation:

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

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

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

Multiply (-9 + a) * (-6 + a)
(-9(-6 + a) + a(-6 + a)) = 0
((-6 * -9 + a * -9) + a(-6 + a)) = 0
((54 + -9a) + a(-6 + a)) = 0
(54 + -9a + (-6 * a + a * a)) = 0
(54 + -9a + (-6a + a2)) = 0

Combine like terms: -9a + -6a = -15a
(54 + -15a + a2) = 0

Solving
54 + -15a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

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

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

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

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

Simplifying
a = 6
Subproblem 2
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

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

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

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

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

Simplifying
a = 9
Solution
a = {6, 9}