12d^2+9=-24d

Solution for 12d^2+9=-24d equation:

Simplifying
12d2 + 9 = -24d

Reorder the terms:
9 + 12d2 = -24d

Solving
9 + 12d2 = -24d

Solving for variable 'd'.

Reorder the terms:
9 + 24d + 12d2 = -24d + 24d

Combine like terms: -24d + 24d = 0
9 + 24d + 12d2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 8d + 4d2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + 2d)' equal to zero and attempt to solve:

Simplifying
3 + 2d = 0

Solving
3 + 2d = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2d = 0 + -3

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

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

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

Simplifying
d = -1.5
Subproblem 2
Set the factor '(1 + 2d)' equal to zero and attempt to solve:

Simplifying
1 + 2d = 0

Solving
1 + 2d = 0

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

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

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

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

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

Simplifying
d = -0.5
Solution
d = {-1.5, -0.5}