k^4-13k^2+42=0

Solution for k^4-13k^2+42=0 equation:

Simplifying
k4 + -13k2 + 42 = 0

Reorder the terms:
42 + -13k2 + k4 = 0

Solving
42 + -13k2 + k4 = 0

Solving for variable 'k'.

Factor a trinomial.
(6 + -1k2)(7 + -1k2) = 0

Subproblem 1
Set the factor '(6 + -1k2)' equal to zero and attempt to solve:

Simplifying
6 + -1k2 = 0

Solving
6 + -1k2 = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k2 = 0 + -6
-1k2 = 0 + -6

Combine like terms: 0 + -6 = -6
-1k2 = -6

Divide each side by '-1'.
k2 = 6

Simplifying
k2 = 6

Take the square root of each side:
k = {-2.449489743, 2.449489743}
Subproblem 2
Set the factor '(7 + -1k2)' equal to zero and attempt to solve:

Simplifying
7 + -1k2 = 0

Solving
7 + -1k2 = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1k2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1k2 = 0 + -7
-1k2 = 0 + -7

Combine like terms: 0 + -7 = -7
-1k2 = -7

Divide each side by '-1'.
k2 = 7

Simplifying
k2 = 7

Take the square root of each side:
k = {-2.645751311, 2.645751311}
Solution
k = {-2.449489743, 2.449489743, -2.645751311, 2.645751311}