3w^4+60w^2-63=0

Solution for 3w^4+60w^2-63=0 equation:

Simplifying
3w4 + 60w2 + -63 = 0

Reorder the terms:
-63 + 60w2 + 3w4 = 0

Solving
-63 + 60w2 + 3w4 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 20w2 + w4) = 0

Factor a trinomial.
3((-21 + -1w2)(1 + -1w2)) = 0

Factor a difference between two squares.
3((-21 + -1w2)((1 + w)(1 + -1w))) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-21 + -1w2)' equal to zero and attempt to solve:

Simplifying
-21 + -1w2 = 0

Solving
-21 + -1w2 = 0

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

Add '21' to each side of the equation.
-21 + 21 + -1w2 = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -1w2 = 0 + 21
-1w2 = 0 + 21

Combine like terms: 0 + 21 = 21
-1w2 = 21

Divide each side by '-1'.
w2 = -21

Simplifying
w2 = -21

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 0

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

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

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

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

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

Simplifying
w = 1
Solution
w = {-1, 1}