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Simplifying (3 + w)(4w + 2) = 0 Reorder the terms: (3 + w)(2 + 4w) = 0 Multiply (3 + w) * (2 + 4w) (3(2 + 4w) + w(2 + 4w)) = 0 ((2 * 3 + 4w * 3) + w(2 + 4w)) = 0 ((6 + 12w) + w(2 + 4w)) = 0 (6 + 12w + (2 * w + 4w * w)) = 0 (6 + 12w + (2w + 4w2)) = 0 Combine like terms: 12w + 2w = 14w (6 + 14w + 4w2) = 0 Solving 6 + 14w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + 7w + 2w2) = 0 Factor a trinomial. 2((3 + w)(1 + 2w)) = 0 Ignore the factor 2.Subproblem 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 '(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 = {-3, -0.5}
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