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Simplifying (3w + 5)(4w + 2) = 0 Reorder the terms: (5 + 3w)(4w + 2) = 0 Reorder the terms: (5 + 3w)(2 + 4w) = 0 Multiply (5 + 3w) * (2 + 4w) (5(2 + 4w) + 3w * (2 + 4w)) = 0 ((2 * 5 + 4w * 5) + 3w * (2 + 4w)) = 0 ((10 + 20w) + 3w * (2 + 4w)) = 0 (10 + 20w + (2 * 3w + 4w * 3w)) = 0 (10 + 20w + (6w + 12w2)) = 0 Combine like terms: 20w + 6w = 26w (10 + 26w + 12w2) = 0 Solving 10 + 26w + 12w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 13w + 6w2) = 0 Factor a trinomial. 2((5 + 3w)(1 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 3w)' equal to zero and attempt to solve: Simplifying 5 + 3w = 0 Solving 5 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3w = 0 + -5 3w = 0 + -5 Combine like terms: 0 + -5 = -5 3w = -5 Divide each side by '3'. w = -1.666666667 Simplifying w = -1.666666667Subproblem 2
Set the factor '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {-1.666666667, -0.5}
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