d^4=16d^2-48

Solution for d^4=16d^2-48 equation:

Simplifying
d4 = 16d2 + -48

Reorder the terms:
d4 = -48 + 16d2

Solving
d4 = -48 + 16d2

Solving for variable 'd'.

Reorder the terms:
48 + -16d2 + d4 = -48 + 16d2 + 48 + -16d2

Reorder the terms:
48 + -16d2 + d4 = -48 + 48 + 16d2 + -16d2

Combine like terms: -48 + 48 = 0
48 + -16d2 + d4 = 0 + 16d2 + -16d2
48 + -16d2 + d4 = 16d2 + -16d2

Combine like terms: 16d2 + -16d2 = 0
48 + -16d2 + d4 = 0

Factor a trinomial.
(4 + -1d2)(12 + -1d2) = 0

Factor a difference between two squares.
((2 + d)(2 + -1d))(12 + -1d2) = 0

Subproblem 1
Set the factor '(12 + -1d2)' equal to zero and attempt to solve:

Simplifying
12 + -1d2 = 0

Solving
12 + -1d2 = 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 + -1d2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1d2 = 0 + -12
-1d2 = 0 + -12

Combine like terms: 0 + -12 = -12
-1d2 = -12

Divide each side by '-1'.
d2 = 12

Simplifying
d2 = 12

Take the square root of each side:
d = {-3.464101615, 3.464101615}
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 = {-3.464101615, 3.464101615, -2, 2}