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Simplifying (3w + -3) * w = 126 Reorder the terms: (-3 + 3w) * w = 126 Reorder the terms for easier multiplication: w(-3 + 3w) = 126 (-3 * w + 3w * w) = 126 (-3w + 3w2) = 126 Solving -3w + 3w2 = 126 Solving for variable 'w'. Reorder the terms: -126 + -3w + 3w2 = 126 + -126 Combine like terms: 126 + -126 = 0 -126 + -3w + 3w2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-42 + -1w + w2) = 0 Factor a trinomial. 3((-6 + -1w)(7 + -1w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 2
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 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 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Solution
w = {-6, 7}
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