9d^4-40d^2+31=0

Solution for 9d^4-40d^2+31=0 equation:

Simplifying
9d4 + -40d2 + 31 = 0

Reorder the terms:
31 + -40d2 + 9d4 = 0

Solving
31 + -40d2 + 9d4 = 0

Solving for variable 'd'.

Factor a trinomial.
(1 + -1d2)(31 + -9d2) = 0

Factor a difference between two squares.
((1 + d)(1 + -1d))(31 + -9d2) = 0

Subproblem 1
Set the factor '(31 + -9d2)' equal to zero and attempt to solve:

Simplifying
31 + -9d2 = 0

Solving
31 + -9d2 = 0

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

Add '-31' to each side of the equation.
31 + -31 + -9d2 = 0 + -31

Combine like terms: 31 + -31 = 0
0 + -9d2 = 0 + -31
-9d2 = 0 + -31

Combine like terms: 0 + -31 = -31
-9d2 = -31

Divide each side by '-9'.
d2 = 3.444444444

Simplifying
d2 = 3.444444444

Take the square root of each side:
d = {-1.855921454, 1.855921454}
Subproblem 2
Set the factor '(1 + d)' equal to zero and attempt to solve:

Simplifying
1 + d = 0

Solving
1 + d = 0

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

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

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

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

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

Simplifying
1 + -1d = 0

Solving
1 + -1d = 0

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

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

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

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

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

Simplifying
d = 1
Solution
d = {-1.855921454, 1.855921454, -1, 1}