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Simplifying (3 + w) * w = 40 Reorder the terms for easier multiplication: w(3 + w) = 40 (3 * w + w * w) = 40 (3w + w^{2}) = 40 Solving 3w + w^{2}= 40 Solving for variable 'w'. Reorder the terms: -40 + 3w + w^{2}= 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 3w + w^{2}= 0 Factor a trinomial. (-8 + -1w)(5 + -1w) = 0## Subproblem 1

Set the factor '(-8 + -1w)' equal to zero and attempt to solve: Simplifying -8 + -1w = 0 Solving -8 + -1w = 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 + -1w = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1w = 0 + 8 -1w = 0 + 8 Combine like terms: 0 + 8 = 8 -1w = 8 Divide each side by '-1'. w = -8 Simplifying w = -8## Subproblem 2

Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 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 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5## Solution

w = {-8, 5}

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