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

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


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

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

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

Multiply (-3 + w) * (-2 + w)
2w(-3(-2 + w) + w(-2 + w)) = 0
2w((-2 * -3 + w * -3) + w(-2 + w)) = 0
2w((6 + -3w) + w(-2 + w)) = 0
2w(6 + -3w + (-2 * w + w * w)) = 0
2w(6 + -3w + (-2w + w2)) = 0

Combine like terms: -3w + -2w = -5w
2w(6 + -5w + w2) = 0
(6 * 2w + -5w * 2w + w2 * 2w) = 0
(12w + -10w2 + 2w3) = 0

Solving
12w + -10w2 + 2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(6 + -5w + w2) = 0

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

Ignore the factor 2.

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 '(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, 2, 3}

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