24d^2+24d+6=0

Solution for 24d^2+24d+6=0 equation:

Simplifying
24d2 + 24d + 6 = 0

Reorder the terms:
6 + 24d + 24d2 = 0

Solving
6 + 24d + 24d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + 4d + 4d2) = 0

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

Ignore the factor 6.
Subproblem 1
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
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 = {-0.5, -0.5}