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

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


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

Remove parenthesis around (3w)
W * 3w = 2w(w + 2)

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

Multiply W * w
3wW = 2w(w + 2)

Reorder the terms:
3wW = 2w(2 + w)
3wW = (2 * 2w + w * 2w)
3wW = (4w + 2w2)

Solving
3wW = 4w + 2w2

Solving for variable 'w'.

Reorder the terms:
-4w + 3wW + -2w2 = 4w + 2w2 + -4w + -2w2

Reorder the terms:
-4w + 3wW + -2w2 = 4w + -4w + 2w2 + -2w2

Combine like terms: 4w + -4w = 0
-4w + 3wW + -2w2 = 0 + 2w2 + -2w2
-4w + 3wW + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-4w + 3wW + -2w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-4 + 3W + -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 '(-4 + 3W + -2w)' equal to zero and attempt to solve:

Simplifying
-4 + 3W + -2w = 0

Solving
-4 + 3W + -2w = 0

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

Add '4' to each side of the equation.
-4 + 3W + 4 + -2w = 0 + 4

Reorder the terms:
-4 + 4 + 3W + -2w = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3W + -2w = 0 + 4
3W + -2w = 0 + 4

Combine like terms: 0 + 4 = 4
3W + -2w = 4

Add '-3W' to each side of the equation.
3W + -3W + -2w = 4 + -3W

Combine like terms: 3W + -3W = 0
0 + -2w = 4 + -3W
-2w = 4 + -3W

Divide each side by '-2'.
w = -2 + 1.5W

Simplifying
w = -2 + 1.5W
Solution
w = {0, -2 + 1.5W}

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