-16d^2+32d+12=24

Solution for -16d^2+32d+12=24 equation:

Simplifying
-16d2 + 32d + 12 = 24

Reorder the terms:
12 + 32d + -16d2 = 24

Solving
12 + 32d + -16d2 = 24

Solving for variable 'd'.

Reorder the terms:
12 + -24 + 32d + -16d2 = 24 + -24

Combine like terms: 12 + -24 = -12
-12 + 32d + -16d2 = 24 + -24

Combine like terms: 24 + -24 = 0
-12 + 32d + -16d2 = 0

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

Factor a trinomial.
4((-3 + 2d)(1 + -2d)) = 0

Ignore the factor 4.
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}