-2w(w-5)(w+2)=0

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Solution for -2w(w-5)(w+2)=0 equation: 


Simplifying
-2w(w + -5)(w + 2) = 0

Reorder the terms:
-2w(-5 + w)(w + 2) = 0

Reorder the terms:
-2w(-5 + w)(2 + w) = 0

Multiply (-5 + w) * (2 + w)
-2w(-5(2 + w) + w(2 + w)) = 0
-2w((2 * -5 + w * -5) + w(2 + w)) = 0
-2w((-10 + -5w) + w(2 + w)) = 0
-2w(-10 + -5w + (2 * w + w * w)) = 0
-2w(-10 + -5w + (2w + w2)) = 0

Combine like terms: -5w + 2w = -3w
-2w(-10 + -3w + w2) = 0
(-10 * -2w + -3w * -2w + w2 * -2w) = 0
(20w + 6w2 + -2w3) = 0

Solving
20w + 6w2 + -2w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(10 + 3w + -1w2) = 0

Factor a trinomial.
2w((5 + -1w)(2 + w)) = 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 '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5

Subproblem 3
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {0, 5, -2}

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