5k^4=45k^2

Solution for 5k^4=45k^2 equation:

Simplifying
5k4 = 45k2

Solving
5k4 = 45k2

Solving for variable 'k'.

Reorder the terms:
-45k2 + 5k4 = 45k2 + -45k2

Combine like terms: 45k2 + -45k2 = 0
-45k2 + 5k4 = 0

Factor out the Greatest Common Factor (GCF), '5k2'.
5k2(-9 + k2) = 0

Factor a difference between two squares.
5k2((3 + k)(-3 + k)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor 'k2' equal to zero and attempt to solve:

Simplifying
k2 = 0

Solving
k2 = 0

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

Simplifying
k2 = 0

Take the square root of each side:
k = {0}
Subproblem 2
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

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

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Subproblem 3
Set the factor '(-3 + k)' equal to zero and attempt to solve:

Simplifying
-3 + k = 0

Solving
-3 + k = 0

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

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

Combine like terms: -3 + 3 = 0
0 + k = 0 + 3
k = 0 + 3

Combine like terms: 0 + 3 = 3
k = 3

Simplifying
k = 3
Solution
k = {0, -3, 3}