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Simplifying (3w + 8)(5 + w) = 0 Reorder the terms: (8 + 3w)(5 + w) = 0 Multiply (8 + 3w) * (5 + w) (8(5 + w) + 3w * (5 + w)) = 0 ((5 * 8 + w * 8) + 3w * (5 + w)) = 0 ((40 + 8w) + 3w * (5 + w)) = 0 (40 + 8w + (5 * 3w + w * 3w)) = 0 (40 + 8w + (15w + 3w2)) = 0 Combine like terms: 8w + 15w = 23w (40 + 23w + 3w2) = 0 Solving 40 + 23w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + w)(8 + 3w) = 0Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5Subproblem 2
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 = -2.666666667Solution
w = {-5, -2.666666667}
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