4k^4+20=42k^2

Solution for 4k^4+20=42k^2 equation:

Simplifying
4k4 + 20 = 42k2

Reorder the terms:
20 + 4k4 = 42k2

Solving
20 + 4k4 = 42k2

Solving for variable 'k'.

Reorder the terms:
20 + -42k2 + 4k4 = 42k2 + -42k2

Combine like terms: 42k2 + -42k2 = 0
20 + -42k2 + 4k4 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -21k2 + 2k4) = 0

Factor a trinomial.
2((1 + -2k2)(10 + -1k2)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + -2k2)' equal to zero and attempt to solve:

Simplifying
1 + -2k2 = 0

Solving
1 + -2k2 = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2k2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2k2 = 0 + -1
-2k2 = 0 + -1

Combine like terms: 0 + -1 = -1
-2k2 = -1

Divide each side by '-2'.
k2 = 0.5

Simplifying
k2 = 0.5

Take the square root of each side:
k = {-0.707106781, 0.707106781}
Subproblem 2
Set the factor '(10 + -1k2)' equal to zero and attempt to solve:

Simplifying
10 + -1k2 = 0

Solving
10 + -1k2 = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k2 = 0 + -10
-1k2 = 0 + -10

Combine like terms: 0 + -10 = -10
-1k2 = -10

Divide each side by '-1'.
k2 = 10

Simplifying
k2 = 10

Take the square root of each side:
k = {-3.16227766, 3.16227766}
Solution
k = {-0.707106781, 0.707106781, -3.16227766, 3.16227766}