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Simplifying (1 + w)(3w + 8) = 0 Reorder the terms: (1 + w)(8 + 3w) = 0 Multiply (1 + w) * (8 + 3w) (1(8 + 3w) + w(8 + 3w)) = 0 ((8 * 1 + 3w * 1) + w(8 + 3w)) = 0 ((8 + 3w) + w(8 + 3w)) = 0 (8 + 3w + (8 * w + 3w * w)) = 0 (8 + 3w + (8w + 3w2)) = 0 Combine like terms: 3w + 8w = 11w (8 + 11w + 3w2) = 0 Solving 8 + 11w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (8 + 3w)(1 + w) = 0Subproblem 1
Set the factor '(8 + 3w)' equal to zero and attempt to solve: Simplifying 8 + 3w = 0 Solving 8 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + 3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 3w = 0 + -8 3w = 0 + -8 Combine like terms: 0 + -8 = -8 3w = -8 Divide each side by '3'. w = -2.666666667 Simplifying w = -2.666666667Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve: Simplifying 1 + w = 0 Solving 1 + w = 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 + w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + w = 0 + -1 w = 0 + -1 Combine like terms: 0 + -1 = -1 w = -1 Simplifying w = -1Solution
w = {-2.666666667, -1}
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