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

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


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

Reorder the terms:
w(2 + w) = (w + -3)(2w)
(2 * w + w * w) = (w + -3)(2w)
(2w + w2) = (w + -3)(2w)

Reorder the terms:
2w + w2 = (-3 + w)(2w)

Remove parenthesis around (2w)
2w + w2 = (-3 + w) * 2w

Reorder the terms for easier multiplication:
2w + w2 = 2w(-3 + w)
2w + w2 = (-3 * 2w + w * 2w)
2w + w2 = (-6w + 2w2)

Solving
2w + w2 = -6w + 2w2

Solving for variable 'w'.

Reorder the terms:
2w + 6w + w2 + -2w2 = -6w + 2w2 + 6w + -2w2

Combine like terms: 2w + 6w = 8w
8w + w2 + -2w2 = -6w + 2w2 + 6w + -2w2

Combine like terms: w2 + -2w2 = -1w2
8w + -1w2 = -6w + 2w2 + 6w + -2w2

Reorder the terms:
8w + -1w2 = -6w + 6w + 2w2 + -2w2

Combine like terms: -6w + 6w = 0
8w + -1w2 = 0 + 2w2 + -2w2
8w + -1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
8w + -1w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(8 + -1w) = 0


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 '(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, 8}

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