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Simplifying (8 + -1w)(4w + 6) = 0 Reorder the terms: (8 + -1w)(6 + 4w) = 0 Multiply (8 + -1w) * (6 + 4w) (8(6 + 4w) + -1w * (6 + 4w)) = 0 ((6 * 8 + 4w * 8) + -1w * (6 + 4w)) = 0 ((48 + 32w) + -1w * (6 + 4w)) = 0 (48 + 32w + (6 * -1w + 4w * -1w)) = 0 (48 + 32w + (-6w + -4w2)) = 0 Combine like terms: 32w + -6w = 26w (48 + 26w + -4w2) = 0 Solving 48 + 26w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 13w + -2w2) = 0 Factor a trinomial. 2((8 + -1w)(3 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve: Simplifying 8 + -1w = 0 Solving 8 + -1w = 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 + -1w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1w = 0 + -8 -1w = 0 + -8 Combine like terms: 0 + -8 = -8 -1w = -8 Divide each side by '-1'. 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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