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Simplifying (4w + 7)(8 + w) = 0 Reorder the terms: (7 + 4w)(8 + w) = 0 Multiply (7 + 4w) * (8 + w) (7(8 + w) + 4w * (8 + w)) = 0 ((8 * 7 + w * 7) + 4w * (8 + w)) = 0 ((56 + 7w) + 4w * (8 + w)) = 0 (56 + 7w + (8 * 4w + w * 4w)) = 0 (56 + 7w + (32w + 4w2)) = 0 Combine like terms: 7w + 32w = 39w (56 + 39w + 4w2) = 0 Solving 56 + 39w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (8 + w)(7 + 4w) = 0Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve: Simplifying 8 + w = 0 Solving 8 + w = 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 + w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + w = 0 + -8 w = 0 + -8 Combine like terms: 0 + -8 = -8 w = -8 Simplifying w = -8Subproblem 2
Set the factor '(7 + 4w)' equal to zero and attempt to solve: Simplifying 7 + 4w = 0 Solving 7 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4w = 0 + -7 4w = 0 + -7 Combine like terms: 0 + -7 = -7 4w = -7 Divide each side by '4'. w = -1.75 Simplifying w = -1.75Solution
w = {-8, -1.75}
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