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Simplifying (9 + -1w)(3w + 1) = 0 Reorder the terms: (9 + -1w)(1 + 3w) = 0 Multiply (9 + -1w) * (1 + 3w) (9(1 + 3w) + -1w * (1 + 3w)) = 0 ((1 * 9 + 3w * 9) + -1w * (1 + 3w)) = 0 ((9 + 27w) + -1w * (1 + 3w)) = 0 (9 + 27w + (1 * -1w + 3w * -1w)) = 0 (9 + 27w + (-1w + -3w2)) = 0 Combine like terms: 27w + -1w = 26w (9 + 26w + -3w2) = 0 Solving 9 + 26w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + -1w)(1 + 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 '(1 + 3w)' equal to zero and attempt to solve: Simplifying 1 + 3w = 0 Solving 1 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3w = 0 + -1 3w = 0 + -1 Combine like terms: 0 + -1 = -1 3w = -1 Divide each side by '3'. w = -0.3333333333 Simplifying w = -0.3333333333Solution
w = {9, -0.3333333333}
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