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

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


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

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

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

Remove parenthesis around (3w)
1w + w2 = 3w(w + -2)

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

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

Solving for variable 'w'.

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

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

Combine like terms: w2 + -3w2 = -2w2
7w + -2w2 = -6w + 3w2 + 6w + -3w2

Reorder the terms:
7w + -2w2 = -6w + 6w + 3w2 + -3w2

Combine like terms: -6w + 6w = 0
7w + -2w2 = 0 + 3w2 + -3w2
7w + -2w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
7w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(7 + -2w) = 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 + -2w)' equal to zero and attempt to solve:

Simplifying
7 + -2w = 0

Solving
7 + -2w = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2w = 0 + -7
-2w = 0 + -7

Combine like terms: 0 + -7 = -7
-2w = -7

Divide each side by '-2'.
w = 3.5

Simplifying
w = 3.5
Solution
w = {0, 3.5}

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