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Simplifying (4 + w)(4w + 9) = 0 Reorder the terms: (4 + w)(9 + 4w) = 0 Multiply (4 + w) * (9 + 4w) (4(9 + 4w) + w(9 + 4w)) = 0 ((9 * 4 + 4w * 4) + w(9 + 4w)) = 0 ((36 + 16w) + w(9 + 4w)) = 0 (36 + 16w + (9 * w + 4w * w)) = 0 (36 + 16w + (9w + 4w2)) = 0 Combine like terms: 16w + 9w = 25w (36 + 25w + 4w2) = 0 Solving 36 + 25w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + w)(9 + 4w) = 0Subproblem 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 '(9 + 4w)' equal to zero and attempt to solve: Simplifying 9 + 4w = 0 Solving 9 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4w = 0 + -9 4w = 0 + -9 Combine like terms: 0 + -9 = -9 4w = -9 Divide each side by '4'. w = -2.25 Simplifying w = -2.25Solution
w = {-4, -2.25}
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