24a^2+84a+72=0

Solution for 24a^2+84a+72=0 equation:

Simplifying
24a2 + 84a + 72 = 0

Reorder the terms:
72 + 84a + 24a2 = 0

Solving
72 + 84a + 24a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '12'.
12(6 + 7a + 2a2) = 0

Factor a trinomial.
12((2 + a)(3 + 2a)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(2 + a)' equal to zero and attempt to solve:

Simplifying
2 + a = 0

Solving
2 + a = 0

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

Add '-2' to each side of the equation.
2 + -2 + a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + a = 0 + -2
a = 0 + -2

Combine like terms: 0 + -2 = -2
a = -2

Simplifying
a = -2
Subproblem 2
Set the factor '(3 + 2a)' equal to zero and attempt to solve:

Simplifying
3 + 2a = 0

Solving
3 + 2a = 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 + 2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2a = 0 + -3
2a = 0 + -3

Combine like terms: 0 + -3 = -3
2a = -3

Divide each side by '2'.
a = -1.5

Simplifying
a = -1.5
Solution
a = {-2, -1.5}