2d^4-13d^2-45=0

Solution for 2d^4-13d^2-45=0 equation:

Simplifying
2d4 + -13d2 + -45 = 0

Reorder the terms:
-45 + -13d2 + 2d4 = 0

Solving
-45 + -13d2 + 2d4 = 0

Solving for variable 'd'.

Factor a trinomial.
(-5 + -2d2)(9 + -1d2) = 0

Factor a difference between two squares.
(-5 + -2d2)((3 + d)(3 + -1d)) = 0

Subproblem 1
Set the factor '(-5 + -2d2)' equal to zero and attempt to solve:

Simplifying
-5 + -2d2 = 0

Solving
-5 + -2d2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2d2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2d2 = 0 + 5
-2d2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2d2 = 5

Divide each side by '-2'.
d2 = -2.5

Simplifying
d2 = -2.5

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(3 + d)' equal to zero and attempt to solve:

Simplifying
3 + d = 0

Solving
3 + d = 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 + d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + d = 0 + -3
d = 0 + -3

Combine like terms: 0 + -3 = -3
d = -3

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

Simplifying
3 + -1d = 0

Solving
3 + -1d = 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 + -1d = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1d = 0 + -3
-1d = 0 + -3

Combine like terms: 0 + -3 = -3
-1d = -3

Divide each side by '-1'.
d = 3

Simplifying
d = 3
Solution
d = {-3, 3}