24g^2+84g+36=0

Solution for 24g^2+84g+36=0 equation:

Simplifying
24g2 + 84g + 36 = 0

Reorder the terms:
36 + 84g + 24g2 = 0

Solving
36 + 84g + 24g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '12'.
12(3 + 7g + 2g2) = 0

Factor a trinomial.
12((3 + g)(1 + 2g)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(3 + g)' equal to zero and attempt to solve:

Simplifying
3 + g = 0

Solving
3 + g = 0

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

Add '-3' to each side of the equation.
3 + -3 + g = 0 + -3

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

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

Simplifying
g = -3
Subproblem 2
Set the factor '(1 + 2g)' equal to zero and attempt to solve:

Simplifying
1 + 2g = 0

Solving
1 + 2g = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2g = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2g = 0 + -1
2g = 0 + -1

Combine like terms: 0 + -1 = -1
2g = -1

Divide each side by '2'.
g = -0.5

Simplifying
g = -0.5
Solution
g = {-3, -0.5}