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Simplifying (3w + -4)(5 + w) = 0 Reorder the terms: (-4 + 3w)(5 + w) = 0 Multiply (-4 + 3w) * (5 + w) (-4(5 + w) + 3w * (5 + w)) = 0 ((5 * -4 + w * -4) + 3w * (5 + w)) = 0 ((-20 + -4w) + 3w * (5 + w)) = 0 (-20 + -4w + (5 * 3w + w * 3w)) = 0 (-20 + -4w + (15w + 3w2)) = 0 Combine like terms: -4w + 15w = 11w (-20 + 11w + 3w2) = 0 Solving -20 + 11w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(4 + -3w) = 0Subproblem 1
Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5Subproblem 2
Set the factor '(4 + -3w)' equal to zero and attempt to solve: Simplifying 4 + -3w = 0 Solving 4 + -3w = 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 + -3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3w = 0 + -4 -3w = 0 + -4 Combine like terms: 0 + -4 = -4 -3w = -4 Divide each side by '-3'. w = 1.333333333 Simplifying w = 1.333333333Solution
w = {-5, 1.333333333}
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