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Simplifying (4 + w)(4w + 2) = 0 Reorder the terms: (4 + w)(2 + 4w) = 0 Multiply (4 + w) * (2 + 4w) (4(2 + 4w) + w(2 + 4w)) = 0 ((2 * 4 + 4w * 4) + w(2 + 4w)) = 0 ((8 + 16w) + w(2 + 4w)) = 0 (8 + 16w + (2 * w + 4w * w)) = 0 (8 + 16w + (2w + 4w2)) = 0 Combine like terms: 16w + 2w = 18w (8 + 18w + 4w2) = 0 Solving 8 + 18w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9w + 2w2) = 0 Factor a trinomial. 2((4 + w)(1 + 2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 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 = {-4, -0.5}
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