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 = -10w
3w(16 + -10w + w2) = 0
(16 * 3w + -10w * 3w + w2 * 3w) = 0
(48w + -30w2 + 3w3) = 0

Solving
48w + -30w2 + 3w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3w'.
3w(16 + -10w + 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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