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Simplifying (8 + w)(3w + 7) = 0 Reorder the terms: (8 + w)(7 + 3w) = 0 Multiply (8 + w) * (7 + 3w) (8(7 + 3w) + w(7 + 3w)) = 0 ((7 * 8 + 3w * 8) + w(7 + 3w)) = 0 ((56 + 24w) + w(7 + 3w)) = 0 (56 + 24w + (7 * w + 3w * w)) = 0 (56 + 24w + (7w + 3w2)) = 0 Combine like terms: 24w + 7w = 31w (56 + 31w + 3w2) = 0 Solving 56 + 31w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (8 + w)(7 + 3w) = 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 + 3w)' equal to zero and attempt to solve: Simplifying 7 + 3w = 0 Solving 7 + 3w = 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 + 3w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3w = 0 + -7 3w = 0 + -7 Combine like terms: 0 + -7 = -7 3w = -7 Divide each side by '3'. w = -2.333333333 Simplifying w = -2.333333333Solution
w = {-8, -2.333333333}
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