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Simplifying (9 + -1w)(2w + -3) = 0 Reorder the terms: (9 + -1w)(-3 + 2w) = 0 Multiply (9 + -1w) * (-3 + 2w) (9(-3 + 2w) + -1w * (-3 + 2w)) = 0 ((-3 * 9 + 2w * 9) + -1w * (-3 + 2w)) = 0 ((-27 + 18w) + -1w * (-3 + 2w)) = 0 (-27 + 18w + (-3 * -1w + 2w * -1w)) = 0 (-27 + 18w + (3w + -2w2)) = 0 Combine like terms: 18w + 3w = 21w (-27 + 21w + -2w2) = 0 Solving -27 + 21w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (-9 + w)(3 + -2w) = 0Subproblem 1
Set the factor '(-9 + w)' equal to zero and attempt to solve: Simplifying -9 + w = 0 Solving -9 + w = 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 + w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w = 0 + 9 w = 0 + 9 Combine like terms: 0 + 9 = 9 w = 9 Simplifying w = 9Subproblem 2
Set the factor '(3 + -2w)' equal to zero and attempt to solve: Simplifying 3 + -2w = 0 Solving 3 + -2w = 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 + -2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2w = 0 + -3 -2w = 0 + -3 Combine like terms: 0 + -3 = -3 -2w = -3 Divide each side by '-2'. w = 1.5 Simplifying w = 1.5Solution
w = {9, 1.5}
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