6w^4-54w^2=0

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Solution for 6w^4-54w^2=0 equation:


Simplifying
6w4 + -54w2 = 0

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

Solving
-54w2 + 6w4 = 0

Solving for variable 'w'.

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

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

Solution

w = {0, -3, 3}

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