(3a-3)(a-6)=

Solution for (3a-3)(a-6)= equation:

Simplifying
(3a + -3)(a + -6) = 0

Reorder the terms:
(-3 + 3a)(a + -6) = 0

Reorder the terms:
(-3 + 3a)(-6 + a) = 0

Multiply (-3 + 3a) * (-6 + a)
(-3(-6 + a) + 3a * (-6 + a)) = 0
((-6 * -3 + a * -3) + 3a * (-6 + a)) = 0
((18 + -3a) + 3a * (-6 + a)) = 0
(18 + -3a + (-6 * 3a + a * 3a)) = 0
(18 + -3a + (-18a + 3a2)) = 0

Combine like terms: -3a + -18a = -21a
(18 + -21a + 3a2) = 0

Solving
18 + -21a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7a + a2) = 0

Factor a trinomial.
3((1 + -1a)(6 + -1a)) = 0

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

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

Simplifying
a = 1
Subproblem 2
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
Solution
a = {1, 6}