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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 = 7w (-36 + 7w + 4w2) = 0 Solving -36 + 7w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-4 + -1w)(9 + -4w) = 0Subproblem 1
Set the factor '(-4 + -1w)' equal to zero and attempt to solve: Simplifying -4 + -1w = 0 Solving -4 + -1w = 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 + -1w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1w = 0 + 4 -1w = 0 + 4 Combine like terms: 0 + 4 = 4 -1w = 4 Divide each side by '-1'. 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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