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Simplifying (-6w + -5)(2w + 9) = 0 Reorder the terms: (-5 + -6w)(2w + 9) = 0 Reorder the terms: (-5 + -6w)(9 + 2w) = 0 Multiply (-5 + -6w) * (9 + 2w) (-5(9 + 2w) + -6w * (9 + 2w)) = 0 ((9 * -5 + 2w * -5) + -6w * (9 + 2w)) = 0 ((-45 + -10w) + -6w * (9 + 2w)) = 0 (-45 + -10w + (9 * -6w + 2w * -6w)) = 0 (-45 + -10w + (-54w + -12w2)) = 0 Combine like terms: -10w + -54w = -64w (-45 + -64w + -12w2) = 0 Solving -45 + -64w + -12w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 64w + 12w2) = 0 Factor a trinomial. -1((9 + 2w)(5 + 6w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 2w)' equal to zero and attempt to solve: Simplifying 9 + 2w = 0 Solving 9 + 2w = 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 + 2w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2w = 0 + -9 2w = 0 + -9 Combine like terms: 0 + -9 = -9 2w = -9 Divide each side by '2'. w = -4.5 Simplifying w = -4.5Subproblem 2
Set the factor '(5 + 6w)' equal to zero and attempt to solve: Simplifying 5 + 6w = 0 Solving 5 + 6w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 6w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 6w = 0 + -5 6w = 0 + -5 Combine like terms: 0 + -5 = -5 6w = -5 Divide each side by '6'. w = -0.8333333333 Simplifying w = -0.8333333333Solution
w = {-4.5, -0.8333333333}
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