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Simplifying (6 + w)(4w + -9) = 0 Reorder the terms: (6 + w)(-9 + 4w) = 0 Multiply (6 + w) * (-9 + 4w) (6(-9 + 4w) + w(-9 + 4w)) = 0 ((-9 * 6 + 4w * 6) + w(-9 + 4w)) = 0 ((-54 + 24w) + w(-9 + 4w)) = 0 (-54 + 24w + (-9 * w + 4w * w)) = 0 (-54 + 24w + (-9w + 4w2)) = 0 Combine like terms: 24w + -9w = 15w (-54 + 15w + 4w2) = 0 Solving -54 + 15w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-6 + -1w)(9 + -4w) = 0Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 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 = {-6, 2.25}
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