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Simplifying (2 + w)(4w + 9) = 0 Reorder the terms: (2 + w)(9 + 4w) = 0 Multiply (2 + w) * (9 + 4w) (2(9 + 4w) + w(9 + 4w)) = 0 ((9 * 2 + 4w * 2) + w(9 + 4w)) = 0 ((18 + 8w) + w(9 + 4w)) = 0 (18 + 8w + (9 * w + 4w * w)) = 0 (18 + 8w + (9w + 4w2)) = 0 Combine like terms: 8w + 9w = 17w (18 + 17w + 4w2) = 0 Solving 18 + 17w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (9 + 4w)(2 + w) = 0Subproblem 1
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 = -2.25Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve: Simplifying 2 + w = 0 Solving 2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + w = 0 + -2 w = 0 + -2 Combine like terms: 0 + -2 = -2 w = -2 Simplifying w = -2Solution
w = {-2.25, -2}
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