=6w^4-54w^2

Solution for =6w^4-54w^2 equation:

Simplifying
0 = 6w4 + -54w2

Reorder the terms:
0 = -54w2 + 6w4

Solving
0 = -54w2 + 6w4

Solving for variable 'w'.
Remove the zero:
54w2 + -6w4 = -54w2 + 6w4 + 54w2 + -6w4

Reorder the terms:
54w2 + -6w4 = -54w2 + 54w2 + 6w4 + -6w4

Combine like terms: -54w2 + 54w2 = 0
54w2 + -6w4 = 0 + 6w4 + -6w4
54w2 + -6w4 = 6w4 + -6w4

Combine like terms: 6w4 + -6w4 = 0
54w2 + -6w4 = 0

Factor out the Greatest Common Factor (GCF), '6w2'.
6w2(9 + -1w2) = 0

Factor a difference between two squares.
6w2((3 + w)(3 + -1w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'w2' equal to zero and attempt to solve:

Simplifying
w2 = 0

Solving
w2 = 0

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

Simplifying
w2 = 0

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

Simplifying
3 + w = 0

Solving
3 + w = 0

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

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

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

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

Simplifying
w = -3
Subproblem 3
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

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