(W+1)(w)=(w-2)(3w)

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Solution for (W+1)(w)=(w-2)(3w) equation: 


Simplifying
(W + 1)(w) = (w + -2)(3w)

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

Reorder the terms for easier multiplication:
w(1 + W) = (w + -2)(3w)
(1 * w + W * w) = (w + -2)(3w)
(1w + wW) = (w + -2)(3w)

Reorder the terms:
1w + wW = (-2 + w)(3w)

Remove parenthesis around (3w)
1w + wW = (-2 + w) * 3w

Reorder the terms for easier multiplication:
1w + wW = 3w(-2 + w)
1w + wW = (-2 * 3w + w * 3w)
1w + wW = (-6w + 3w2)

Solving
1w + wW = -6w + 3w2

Solving for variable 'w'.

Reorder the terms:
1w + 6w + wW + -3w2 = -6w + 3w2 + 6w + -3w2

Combine like terms: 1w + 6w = 7w
7w + wW + -3w2 = -6w + 3w2 + 6w + -3w2

Reorder the terms:
7w + wW + -3w2 = -6w + 6w + 3w2 + -3w2

Combine like terms: -6w + 6w = 0
7w + wW + -3w2 = 0 + 3w2 + -3w2
7w + wW + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
7w + wW + -3w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(7 + W + -3w) = 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 '(7 + W + -3w)' equal to zero and attempt to solve:

Simplifying
7 + W + -3w = 0

Solving
7 + W + -3w = 0

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

Add '-7' to each side of the equation.
7 + W + -7 + -3w = 0 + -7

Reorder the terms:
7 + -7 + W + -3w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + W + -3w = 0 + -7
W + -3w = 0 + -7

Combine like terms: 0 + -7 = -7
W + -3w = -7

Add '-1W' to each side of the equation.
W + -1W + -3w = -7 + -1W

Combine like terms: W + -1W = 0
0 + -3w = -7 + -1W
-3w = -7 + -1W

Divide each side by '-3'.
w = 2.333333333 + 0.3333333333W

Simplifying
w = 2.333333333 + 0.3333333333W
Solution
w = {0, 2.333333333 + 0.3333333333W}

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