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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 + -1w + 3w2 + -1w2 = 1w + w2 + -1w + -1w2 Combine like terms: -6w + -1w = -7w -7w + 3w2 + -1w2 = 1w + w2 + -1w + -1w2 Combine like terms: 3w2 + -1w2 = 2w2 -7w + 2w2 = 1w + w2 + -1w + -1w2 Reorder the terms: -7w + 2w2 = 1w + -1w + w2 + -1w2 Combine like terms: 1w + -1w = 0 -7w + 2w2 = 0 + w2 + -1w2 -7w + 2w2 = w2 + -1w2 Combine like terms: w2 + -1w2 = 0 -7w + 2w2 = 0 Factor out the Greatest Common Factor (GCF), 'w'. w(-7 + 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 '(-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 = 3.5Solution
w = {0, 3.5}
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