2(d^2-4d-192)=0

Solution for 2(d^2-4d-192)=0 equation:

Simplifying
2(d2 + -4d + -192) = 0

Reorder the terms:
2(-192 + -4d + d2) = 0
(-192 * 2 + -4d * 2 + d2 * 2) = 0
(-384 + -8d + 2d2) = 0

Solving
-384 + -8d + 2d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-192 + -4d + d2) = 0

Factor a trinomial.
2((-12 + -1d)(16 + -1d)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-12 + -1d)' equal to zero and attempt to solve:

Simplifying
-12 + -1d = 0

Solving
-12 + -1d = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1d = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1d = 0 + 12
-1d = 0 + 12

Combine like terms: 0 + 12 = 12
-1d = 12

Divide each side by '-1'.
d = -12

Simplifying
d = -12
Subproblem 2
Set the factor '(16 + -1d)' equal to zero and attempt to solve:

Simplifying
16 + -1d = 0

Solving
16 + -1d = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1d = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1d = 0 + -16
-1d = 0 + -16

Combine like terms: 0 + -16 = -16
-1d = -16

Divide each side by '-1'.
d = 16

Simplifying
d = 16
Solution
d = {-12, 16}