3a^2+15a=72

Solution for 3a^2+15a=72 equation:

Simplifying
3a2 + 15a = 72

Reorder the terms:
15a + 3a2 = 72

Solving
15a + 3a2 = 72

Solving for variable 'a'.

Reorder the terms:
-72 + 15a + 3a2 = 72 + -72

Combine like terms: 72 + -72 = 0
-72 + 15a + 3a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-24 + 5a + a2) = 0

Factor a trinomial.
3((-8 + -1a)(3 + -1a)) = 0

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

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 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 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
a = -8

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