(2a+2)(3a-9)=0

Solution for (2a+2)(3a-9)=0 equation:

Simplifying
(2a + 2)(3a + -9) = 0

Reorder the terms:
(2 + 2a)(3a + -9) = 0

Reorder the terms:
(2 + 2a)(-9 + 3a) = 0

Multiply (2 + 2a) * (-9 + 3a)
(2(-9 + 3a) + 2a * (-9 + 3a)) = 0
((-9 * 2 + 3a * 2) + 2a * (-9 + 3a)) = 0
((-18 + 6a) + 2a * (-9 + 3a)) = 0
(-18 + 6a + (-9 * 2a + 3a * 2a)) = 0
(-18 + 6a + (-18a + 6a2)) = 0

Combine like terms: 6a + -18a = -12a
(-18 + -12a + 6a2) = 0

Solving
-18 + -12a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + -2a + a2) = 0

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

Ignore the factor 6.
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 '(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
Solution
a = {-1, 3}