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Simplifying (3 + w)(3w + 8) = 0 Reorder the terms: (3 + w)(8 + 3w) = 0 Multiply (3 + w) * (8 + 3w) (3(8 + 3w) + w(8 + 3w)) = 0 ((8 * 3 + 3w * 3) + w(8 + 3w)) = 0 ((24 + 9w) + w(8 + 3w)) = 0 (24 + 9w + (8 * w + 3w * w)) = 0 (24 + 9w + (8w + 3w2)) = 0 Combine like terms: 9w + 8w = 17w (24 + 17w + 3w2) = 0 Solving 24 + 17w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (3 + w)(8 + 3w) = 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 + 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 = {-3, -2.666666667}
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