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Simplifying (3 + w)(5w + 8) = 0 Reorder the terms: (3 + w)(8 + 5w) = 0 Multiply (3 + w) * (8 + 5w) (3(8 + 5w) + w(8 + 5w)) = 0 ((8 * 3 + 5w * 3) + w(8 + 5w)) = 0 ((24 + 15w) + w(8 + 5w)) = 0 (24 + 15w + (8 * w + 5w * w)) = 0 (24 + 15w + (8w + 5w2)) = 0 Combine like terms: 15w + 8w = 23w (24 + 23w + 5w2) = 0 Solving 24 + 23w + 5w2 = 0 Solving for variable 'w'. Factor a trinomial. (3 + w)(8 + 5w) = 0Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve: Simplifying 3 + w = 0 Solving 3 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + w = 0 + -3 w = 0 + -3 Combine like terms: 0 + -3 = -3 w = -3 Simplifying w = -3Subproblem 2
Set the factor '(8 + 5w)' equal to zero and attempt to solve: Simplifying 8 + 5w = 0 Solving 8 + 5w = 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 + 5w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 5w = 0 + -8 5w = 0 + -8 Combine like terms: 0 + -8 = -8 5w = -8 Divide each side by '5'. w = -1.6 Simplifying w = -1.6Solution
w = {-3, -1.6}
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