4d^2+9=-12d

Solution for 4d^2+9=-12d equation:

Simplifying
4d2 + 9 = -12d

Reorder the terms:
9 + 4d2 = -12d

Solving
9 + 4d2 = -12d

Solving for variable 'd'.

Reorder the terms:
9 + 12d + 4d2 = -12d + 12d

Combine like terms: -12d + 12d = 0
9 + 12d + 4d2 = 0

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

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 '(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
Solution
d = {-1.5, -1.5}