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Simplifying (3w + -8)(5 + w) = 0 Reorder the terms: (-8 + 3w)(5 + w) = 0 Multiply (-8 + 3w) * (5 + w) (-8(5 + w) + 3w * (5 + w)) = 0 ((5 * -8 + w * -8) + 3w * (5 + w)) = 0 ((-40 + -8w) + 3w * (5 + w)) = 0 (-40 + -8w + (5 * 3w + w * 3w)) = 0 (-40 + -8w + (15w + 3w2)) = 0 Combine like terms: -8w + 15w = 7w (-40 + 7w + 3w2) = 0 Solving -40 + 7w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-5 + -1w)(8 + -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 '(8 + -3w)' equal to zero and attempt to solve: Simplifying 8 + -3w = 0 Solving 8 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -3w = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3w = 0 + -8 -3w = 0 + -8 Combine like terms: 0 + -8 = -8 -3w = -8 Divide each side by '-3'. w = 2.666666667 Simplifying w = 2.666666667Solution
w = {-5, 2.666666667}
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