12d^2+90d+78=0

Solution for 12d^2+90d+78=0 equation:

Simplifying
12d2 + 90d + 78 = 0

Reorder the terms:
78 + 90d + 12d2 = 0

Solving
78 + 90d + 12d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '6'.
6(13 + 15d + 2d2) = 0

Factor a trinomial.
6((13 + 2d)(1 + d)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(13 + 2d)' equal to zero and attempt to solve:

Simplifying
13 + 2d = 0

Solving
13 + 2d = 0

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

Add '-13' to each side of the equation.
13 + -13 + 2d = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 2d = 0 + -13
2d = 0 + -13

Combine like terms: 0 + -13 = -13
2d = -13

Divide each side by '2'.
d = -6.5

Simplifying
d = -6.5
Subproblem 2
Set the factor '(1 + d)' equal to zero and attempt to solve:

Simplifying
1 + d = 0

Solving
1 + d = 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 + d = 0 + -1

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

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

Simplifying
d = -1
Solution
d = {-6.5, -1}