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Simplifying (4w + -6)(9 + -1w) = 0 Reorder the terms: (-6 + 4w)(9 + -1w) = 0 Multiply (-6 + 4w) * (9 + -1w) (-6(9 + -1w) + 4w * (9 + -1w)) = 0 ((9 * -6 + -1w * -6) + 4w * (9 + -1w)) = 0 ((-54 + 6w) + 4w * (9 + -1w)) = 0 (-54 + 6w + (9 * 4w + -1w * 4w)) = 0 (-54 + 6w + (36w + -4w2)) = 0 Combine like terms: 6w + 36w = 42w (-54 + 42w + -4w2) = 0 Solving -54 + 42w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + 21w + -2w2) = 0 Factor a trinomial. 2((-9 + w)(3 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + w)' equal to zero and attempt to solve: Simplifying -9 + w = 0 Solving -9 + w = 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 + w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w = 0 + 9 w = 0 + 9 Combine like terms: 0 + 9 = 9 w = 9 Simplifying w = 9Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {9, 1.5}
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