4k^4=9k^2

Solution for 4k^4=9k^2 equation:

Simplifying
4k4 = 9k2

Solving
4k4 = 9k2

Solving for variable 'k'.

Reorder the terms:
-9k2 + 4k4 = 9k2 + -9k2

Combine like terms: 9k2 + -9k2 = 0
-9k2 + 4k4 = 0

Factor out the Greatest Common Factor (GCF), 'k2'.
k2(-9 + 4k2) = 0

Factor a difference between two squares.
k2((3 + 2k)(-3 + 2k)) = 0

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 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 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 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Subproblem 3
Set the factor '(-3 + 2k)' equal to zero and attempt to solve:

Simplifying
-3 + 2k = 0

Solving
-3 + 2k = 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 + 2k = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2k = 0 + 3
2k = 0 + 3

Combine like terms: 0 + 3 = 3
2k = 3

Divide each side by '2'.
k = 1.5

Simplifying
k = 1.5
Solution
k = {0, -1.5, 1.5}