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Simplifying (3w + -2)(9 + w) = 0 Reorder the terms: (-2 + 3w)(9 + w) = 0 Multiply (-2 + 3w) * (9 + w) (-2(9 + w) + 3w * (9 + w)) = 0 ((9 * -2 + w * -2) + 3w * (9 + w)) = 0 ((-18 + -2w) + 3w * (9 + w)) = 0 (-18 + -2w + (9 * 3w + w * 3w)) = 0 (-18 + -2w + (27w + 3w2)) = 0 Combine like terms: -2w + 27w = 25w (-18 + 25w + 3w2) = 0 Solving -18 + 25w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + -1w)(2 + -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 '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667Solution
w = {-9, 0.6666666667}
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