-d^4+16d^2-48=0

Solution for -d^4+16d^2-48=0 equation:

Simplifying
-1d4 + 16d2 + -48 = 0

Reorder the terms:
-48 + 16d2 + -1d4 = 0

Solving
-48 + 16d2 + -1d4 = 0

Solving for variable 'd'.

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

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

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

Simplifying
-12 + d2 = 0

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

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

Combine like terms: 0 + 12 = 12
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}