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Simplifying 7w(8w + -9)(w + 6) = 0 Reorder the terms: 7w(-9 + 8w)(w + 6) = 0 Reorder the terms: 7w(-9 + 8w)(6 + w) = 0 Multiply (-9 + 8w) * (6 + w) 7w(-9(6 + w) + 8w * (6 + w)) = 0 7w((6 * -9 + w * -9) + 8w * (6 + w)) = 0 7w((-54 + -9w) + 8w * (6 + w)) = 0 7w(-54 + -9w + (6 * 8w + w * 8w)) = 0 7w(-54 + -9w + (48w + 8w2)) = 0 Combine like terms: -9w + 48w = 39w 7w(-54 + 39w + 8w2) = 0 (-54 * 7w + 39w * 7w + 8w2 * 7w) = 0 (-378w + 273w2 + 56w3) = 0 Solving -378w + 273w2 + 56w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '7w'. 7w(-54 + 39w + 8w2) = 0 Factor a trinomial. 7w((-6 + -1w)(9 + -8w)) = 0 Ignore the factor 7.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 = 0Subproblem 2
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 3
Set the factor '(9 + -8w)' equal to zero and attempt to solve: Simplifying 9 + -8w = 0 Solving 9 + -8w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -8w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8w = 0 + -9 -8w = 0 + -9 Combine like terms: 0 + -9 = -9 -8w = -9 Divide each side by '-8'. w = 1.125 Simplifying w = 1.125Solution
w = {0, -6, 1.125}
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