7x^4-41x^2+30=0

Solution for 7x^4-41x^2+30=0 equation:

Simplifying
7x4 + -41x2 + 30 = 0

Reorder the terms:
30 + -41x2 + 7x4 = 0

Solving
30 + -41x2 + 7x4 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -7x2)(5 + -1x2) = 0

Subproblem 1
Set the factor '(6 + -7x2)' equal to zero and attempt to solve:

Simplifying
6 + -7x2 = 0

Solving
6 + -7x2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7x2 = 0 + -6
-7x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-7x2 = -6

Divide each side by '-7'.
x2 = 0.8571428571

Simplifying
x2 = 0.8571428571

Take the square root of each side:
x = {-0.9258201, 0.9258201}
Subproblem 2
Set the factor '(5 + -1x2)' equal to zero and attempt to solve:

Simplifying
5 + -1x2 = 0

Solving
5 + -1x2 = 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 + -1x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x2 = 0 + -5
-1x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-1x2 = -5

Divide each side by '-1'.
x2 = 5

Simplifying
x2 = 5

Take the square root of each side:
x = {-2.236067978, 2.236067978}
Solution
x = {-0.9258201, 0.9258201, -2.236067978, 2.236067978}