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Simplifying (9 + w)(3w + -5) = 0 Reorder the terms: (9 + w)(-5 + 3w) = 0 Multiply (9 + w) * (-5 + 3w) (9(-5 + 3w) + w(-5 + 3w)) = 0 ((-5 * 9 + 3w * 9) + w(-5 + 3w)) = 0 ((-45 + 27w) + w(-5 + 3w)) = 0 (-45 + 27w + (-5 * w + 3w * w)) = 0 (-45 + 27w + (-5w + 3w2)) = 0 Combine like terms: 27w + -5w = 22w (-45 + 22w + 3w2) = 0 Solving -45 + 22w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(5 + -3w) = 0Subproblem 1
Set the factor '(-9 + -1w)' equal to zero and attempt to solve: Simplifying -9 + -1w = 0 Solving -9 + -1w = 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 + -1w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1w = 0 + 9 -1w = 0 + 9 Combine like terms: 0 + 9 = 9 -1w = 9 Divide each side by '-1'. w = -9 Simplifying w = -9Subproblem 2
Set the factor '(5 + -3w)' equal to zero and attempt to solve: Simplifying 5 + -3w = 0 Solving 5 + -3w = 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 + -3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3w = 0 + -5 -3w = 0 + -5 Combine like terms: 0 + -5 = -5 -3w = -5 Divide each side by '-3'. w = 1.666666667 Simplifying w = 1.666666667Solution
w = {-9, 1.666666667}
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