d^4+32-12d^2=0

Solution for d^4+32-12d^2=0 equation:

Simplifying
d4 + 32 + -12d2 = 0

Reorder the terms:
32 + -12d2 + d4 = 0

Solving
32 + -12d2 + d4 = 0

Solving for variable 'd'.

Factor a trinomial.
(4 + -1d2)(8 + -1d2) = 0

Factor a difference between two squares.
((2 + d)(2 + -1d))(8 + -1d2) = 0

Subproblem 1
Set the factor '(8 + -1d2)' equal to zero and attempt to solve:

Simplifying
8 + -1d2 = 0

Solving
8 + -1d2 = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1d2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1d2 = 0 + -8
-1d2 = 0 + -8

Combine like terms: 0 + -8 = -8
-1d2 = -8

Divide each side by '-1'.
d2 = 8

Simplifying
d2 = 8

Take the square root of each side:
d = {-2.828427125, 2.828427125}
Subproblem 2
Set the factor '(2 + d)' equal to zero and attempt to solve:

Simplifying
2 + d = 0

Solving
2 + d = 0

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

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

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

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

Simplifying
d = -2
Subproblem 3
Set the factor '(2 + -1d)' equal to zero and attempt to solve:

Simplifying
2 + -1d = 0

Solving
2 + -1d = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1d = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1d = 0 + -2
-1d = 0 + -2

Combine like terms: 0 + -2 = -2
-1d = -2

Divide each side by '-1'.
d = 2

Simplifying
d = 2
Solution
d = {-2.828427125, 2.828427125, -2, 2}