3a^2+72=-33a

Solution for 3a^2+72=-33a equation:

Simplifying
3a2 + 72 = -33a

Reorder the terms:
72 + 3a2 = -33a

Solving
72 + 3a2 = -33a

Solving for variable 'a'.

Reorder the terms:
72 + 33a + 3a2 = -33a + 33a

Combine like terms: -33a + 33a = 0
72 + 33a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 11a + a2) = 0

Factor a trinomial.
3((8 + a)(3 + a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve:

Simplifying
8 + a = 0

Solving
8 + a = 0

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

Add '-8' to each side of the equation.
8 + -8 + a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + a = 0 + -8
a = 0 + -8

Combine like terms: 0 + -8 = -8
a = -8

Simplifying
a = -8
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 = {-8, -3}