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Simplifying (5 + w)(4w + -9) = 0 Reorder the terms: (5 + w)(-9 + 4w) = 0 Multiply (5 + w) * (-9 + 4w) (5(-9 + 4w) + w(-9 + 4w)) = 0 ((-9 * 5 + 4w * 5) + w(-9 + 4w)) = 0 ((-45 + 20w) + w(-9 + 4w)) = 0 (-45 + 20w + (-9 * w + 4w * w)) = 0 (-45 + 20w + (-9w + 4w2)) = 0 Combine like terms: 20w + -9w = 11w (-45 + 11w + 4w2) = 0 Solving -45 + 11w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(9 + -4w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 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 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(9 + -4w)' equal to zero and attempt to solve: Simplifying 9 + -4w = 0 Solving 9 + -4w = 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 + -4w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4w = 0 + -9 -4w = 0 + -9 Combine like terms: 0 + -9 = -9 -4w = -9 Divide each side by '-4'. w = 2.25 Simplifying w = 2.25Solution
w = {-5, 2.25}
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