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Simplifying (2w + 9)(w + -3) = 0 Reorder the terms: (9 + 2w)(w + -3) = 0 Reorder the terms: (9 + 2w)(-3 + w) = 0 Multiply (9 + 2w) * (-3 + w) (9(-3 + w) + 2w * (-3 + w)) = 0 ((-3 * 9 + w * 9) + 2w * (-3 + w)) = 0 ((-27 + 9w) + 2w * (-3 + w)) = 0 (-27 + 9w + (-3 * 2w + w * 2w)) = 0 (-27 + 9w + (-6w + 2w2)) = 0 Combine like terms: 9w + -6w = 3w (-27 + 3w + 2w2) = 0 Solving -27 + 3w + 2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -2w)(3 + -1w) = 0Subproblem 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 '(3 + -1w)' equal to zero and attempt to solve: Simplifying 3 + -1w = 0 Solving 3 + -1w = 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 + -1w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1w = 0 + -3 -1w = 0 + -3 Combine like terms: 0 + -3 = -3 -1w = -3 Divide each side by '-1'. w = 3 Simplifying w = 3Solution
w = {-4.5, 3}
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