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Simplifying (4w + 6)(8 + w) = 0 Reorder the terms: (6 + 4w)(8 + w) = 0 Multiply (6 + 4w) * (8 + w) (6(8 + w) + 4w * (8 + w)) = 0 ((8 * 6 + w * 6) + 4w * (8 + w)) = 0 ((48 + 6w) + 4w * (8 + w)) = 0 (48 + 6w + (8 * 4w + w * 4w)) = 0 (48 + 6w + (32w + 4w2)) = 0 Combine like terms: 6w + 32w = 38w (48 + 38w + 4w2) = 0 Solving 48 + 38w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 19w + 2w2) = 0 Factor a trinomial. 2((8 + w)(3 + 2w)) = 0 Ignore the factor 2.Subproblem 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 '(3 + 2w)' equal to zero and attempt to solve: Simplifying 3 + 2w = 0 Solving 3 + 2w = 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 + 2w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2w = 0 + -3 2w = 0 + -3 Combine like terms: 0 + -3 = -3 2w = -3 Divide each side by '2'. w = -1.5 Simplifying w = -1.5Solution
w = {-8, -1.5}
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