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Simplifying -3(w + -7)(-1w + 1) = 0 Reorder the terms: -3(-7 + w)(-1w + 1) = 0 Reorder the terms: -3(-7 + w)(1 + -1w) = 0 Multiply (-7 + w) * (1 + -1w) -3(-7(1 + -1w) + w(1 + -1w)) = 0 -3((1 * -7 + -1w * -7) + w(1 + -1w)) = 0 -3((-7 + 7w) + w(1 + -1w)) = 0 -3(-7 + 7w + (1 * w + -1w * w)) = 0 -3(-7 + 7w + (1w + -1w2)) = 0 Combine like terms: 7w + 1w = 8w -3(-7 + 8w + -1w2) = 0 (-7 * -3 + 8w * -3 + -1w2 * -3) = 0 (21 + -24w + 3w2) = 0 Solving 21 + -24w + 3w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + -8w + w2) = 0 Factor a trinomial. 3((1 + -1w)(7 + -1w)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Subproblem 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 = {1, 7}
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