x^4-13x^2+30=0

Solution for x^4-13x^2+30=0 equation:

Simplifying
x4 + -13x2 + 30 = 0

Reorder the terms:
30 + -13x2 + x4 = 0

Solving
30 + -13x2 + x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x2)(10 + -1x2) = 0

Subproblem 1
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}
Subproblem 2
Set the factor '(10 + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + -1x2 = 0

Solving
10 + -1x2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x2 = 0 + -10
-1x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1x2 = -10

Divide each side by '-1'.
x2 = 10

Simplifying
x2 = 10

Take the square root of each side:
x = {-3.16227766, 3.16227766}
Solution
x = {-1.732050808, 1.732050808, -3.16227766, 3.16227766}