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

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


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

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

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

Multiply w * w
3w2 = (w + 2)(2w)

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

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

Reorder the terms for easier multiplication:
3w2 = 2w(2 + w)
3w2 = (2 * 2w + w * 2w)
3w2 = (4w + 2w2)

Solving
3w2 = 4w + 2w2

Solving for variable 'w'.

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

Combine like terms: 3w2 + -2w2 = 1w2
-4w + 1w2 = 4w + 2w2 + -4w + -2w2

Reorder the terms:
-4w + 1w2 = 4w + -4w + 2w2 + -2w2

Combine like terms: 4w + -4w = 0
-4w + 1w2 = 0 + 2w2 + -2w2
-4w + 1w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
-4w + 1w2 = 0

Factor out the Greatest Common Factor (GCF), 'w'.
w(-4 + w) = 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 + w)' equal to zero and attempt to solve: Simplifying -4 + w = 0 Solving -4 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w = 0 + 4 w = 0 + 4 Combine like terms: 0 + 4 = 4 w = 4 Simplifying w = 4

Solution

w = {0, 4}

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