(3a-9)(a-9)=0

Solution for (3a-9)(a-9)=0 equation:

Simplifying
(3a + -9)(a + -9) = 0

Reorder the terms:
(-9 + 3a)(a + -9) = 0

Reorder the terms:
(-9 + 3a)(-9 + a) = 0

Multiply (-9 + 3a) * (-9 + a)
(-9(-9 + a) + 3a * (-9 + a)) = 0
((-9 * -9 + a * -9) + 3a * (-9 + a)) = 0
((81 + -9a) + 3a * (-9 + a)) = 0
(81 + -9a + (-9 * 3a + a * 3a)) = 0
(81 + -9a + (-27a + 3a2)) = 0

Combine like terms: -9a + -27a = -36a
(81 + -36a + 3a2) = 0

Solving
81 + -36a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -12a + a2) = 0

Factor a trinomial.
3((3 + -1a)(9 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
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 = {3, 9}