=x^4-8x^2+15

Solution for =x^4-8x^2+15 equation:

Simplifying
0 = x4 + -8x2 + 15

Reorder the terms:
0 = 15 + -8x2 + x4

Solving
0 = 15 + -8x2 + x4

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + 8x2 + -1x4 = 15 + -8x2 + x4 + -15 + 8x2 + -1x4

Reorder the terms:
-15 + 8x2 + -1x4 = 15 + -15 + -8x2 + 8x2 + x4 + -1x4

Combine like terms: 15 + -15 = 0
-15 + 8x2 + -1x4 = 0 + -8x2 + 8x2 + x4 + -1x4
-15 + 8x2 + -1x4 = -8x2 + 8x2 + x4 + -1x4

Combine like terms: -8x2 + 8x2 = 0
-15 + 8x2 + -1x4 = 0 + x4 + -1x4
-15 + 8x2 + -1x4 = x4 + -1x4

Combine like terms: x4 + -1x4 = 0
-15 + 8x2 + -1x4 = 0

Factor a trinomial.
(-5 + x2)(3 + -1x2) = 0

Subproblem 1
Set the factor '(-5 + x2)' equal to zero and attempt to solve:

Simplifying
-5 + x2 = 0

Solving
-5 + x2 = 0

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

Add '5' to each side of the equation.
-5 + 5 + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x2 = 0 + 5
x2 = 0 + 5

Combine like terms: 0 + 5 = 5
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Subproblem 2
Set the factor '(3 + -1x2)' equal to zero and attempt to solve:

Simplifying
3 + -1x2 = 0

Solving
3 + -1x2 = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x2 = 0 + -3
-1x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-1x2 = -3

Divide each side by '-1'.
x2 = 3

Simplifying
x2 = 3

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