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Simplifying 3w(w + -2) = w(w + -1) Reorder the terms: 3w(-2 + w) = w(w + -1) (-2 * 3w + w * 3w) = w(w + -1) (-6w + 3w2) = w(w + -1) Reorder the terms: -6w + 3w2 = w(-1 + w) -6w + 3w2 = (-1 * w + w * w) -6w + 3w2 = (-1w + w2) Solving -6w + 3w2 = -1w + w2 Solving for variable 'w'. Reorder the terms: -6w + w + 3w2 + -1w2 = -1w + w2 + w + -1w2 Combine like terms: -6w + w = -5w -5w + 3w2 + -1w2 = -1w + w2 + w + -1w2 Combine like terms: 3w2 + -1w2 = 2w2 -5w + 2w2 = -1w + w2 + w + -1w2 Reorder the terms: -5w + 2w2 = -1w + w + w2 + -1w2 Combine like terms: -1w + w = 0 -5w + 2w2 = 0 + w2 + -1w2 -5w + 2w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -5w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(-5 + 2w) = 0Subproblem 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 = 0Subproblem 2
Set the factor '(-5 + 2w)' equal to zero and attempt to solve: Simplifying -5 + 2w = 0 Solving -5 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + 2w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2w = 0 + 5 2w = 0 + 5 Combine like terms: 0 + 5 = 5 2w = 5 Divide each side by '2'. w = 2.5 Simplifying w = 2.5Solution
w = {0, 2.5}
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