r^4-8r^2=-15

Solution for r^4-8r^2=-15 equation:

Simplifying
r4 + -8r2 = -15

Reorder the terms:
-8r2 + r4 = -15

Solving
-8r2 + r4 = -15

Solving for variable 'r'.

Reorder the terms:
15 + -8r2 + r4 = -15 + 15

Combine like terms: -15 + 15 = 0
15 + -8r2 + r4 = 0

Factor a trinomial.
(3 + -1r2)(5 + -1r2) = 0

Subproblem 1
Set the factor '(3 + -1r2)' equal to zero and attempt to solve:

Simplifying
3 + -1r2 = 0

Solving
3 + -1r2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1r2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1r2 = 0 + -3
-1r2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1r2 = -3

Divide each side by '-1'.
r2 = 3

Simplifying
r2 = 3

Take the square root of each side:
r = {-1.732050808, 1.732050808}
Subproblem 2
Set the factor '(5 + -1r2)' equal to zero and attempt to solve:

Simplifying
5 + -1r2 = 0

Solving
5 + -1r2 = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1r2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1r2 = 0 + -5
-1r2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1r2 = -5

Divide each side by '-1'.
r2 = 5

Simplifying
r2 = 5

Take the square root of each side:
r = {-2.236067978, 2.236067978}
Solution
r = {-1.732050808, 1.732050808, -2.236067978, 2.236067978}