3w(w-8)(w+2)=0

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Solution for 3w(w-8)(w+2)=0 equation: 


Simplifying
3w(w + -8)(w + 2) = 0

Reorder the terms:
3w(-8 + w)(w + 2) = 0

Reorder the terms:
3w(-8 + w)(2 + w) = 0

Multiply (-8 + w) * (2 + w)
3w(-8(2 + w) + w(2 + w)) = 0
3w((2 * -8 + w * -8) + w(2 + w)) = 0
3w((-16 + -8w) + w(2 + w)) = 0
3w(-16 + -8w + (2 * w + w * w)) = 0
3w(-16 + -8w + (2w + w2)) = 0

Combine like terms: -8w + 2w = -6w
3w(-16 + -6w + w2) = 0
(-16 * 3w + -6w * 3w + w2 * 3w) = 0
(-48w + -18w2 + 3w3) = 0

Solving
-48w + -18w2 + 3w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(-16 + -6w + w2) = 0

Factor a trinomial.
3w((-2 + -1w)(8 + -1w)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

Subproblem 2
Set the factor '(-2 + -1w)' equal to zero and attempt to solve:

Simplifying
-2 + -1w = 0

Solving
-2 + -1w = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1w = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1w = 0 + 2
-1w = 0 + 2

Combine like terms: 0 + 2 = 2
-1w = 2

Divide each side by '-1'.
w = -2

Simplifying
w = -2

Subproblem 3
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {0, -2, 8}

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