(-a+6)(3a+9)=

Solution for (-a+6)(3a+9)= equation:

Simplifying
(-1a + 6)(3a + 9) = 0

Reorder the terms:
(6 + -1a)(3a + 9) = 0

Reorder the terms:
(6 + -1a)(9 + 3a) = 0

Multiply (6 + -1a) * (9 + 3a)
(6(9 + 3a) + -1a * (9 + 3a)) = 0
((9 * 6 + 3a * 6) + -1a * (9 + 3a)) = 0
((54 + 18a) + -1a * (9 + 3a)) = 0
(54 + 18a + (9 * -1a + 3a * -1a)) = 0
(54 + 18a + (-9a + -3a2)) = 0

Combine like terms: 18a + -9a = 9a
(54 + 9a + -3a2) = 0

Solving
54 + 9a + -3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + 3a + -1a2) = 0

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

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

Simplifying
3 + a = 0

Solving
3 + a = 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 + a = 0 + -3

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

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

Simplifying
a = -3
Solution
a = {6, -3}