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Simplifying (4 + -1w)(4w + 6) = 0 Reorder the terms: (4 + -1w)(6 + 4w) = 0 Multiply (4 + -1w) * (6 + 4w) (4(6 + 4w) + -1w * (6 + 4w)) = 0 ((6 * 4 + 4w * 4) + -1w * (6 + 4w)) = 0 ((24 + 16w) + -1w * (6 + 4w)) = 0 (24 + 16w + (6 * -1w + 4w * -1w)) = 0 (24 + 16w + (-6w + -4w2)) = 0 Combine like terms: 16w + -6w = 10w (24 + 10w + -4w2) = 0 Solving 24 + 10w + -4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + 5w + -2w2) = 0 Factor a trinomial. 2((4 + -1w)(3 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 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 = {4, -1.5}
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