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Simplifying (7 + w)(4w + -5) = 0 Reorder the terms: (7 + w)(-5 + 4w) = 0 Multiply (7 + w) * (-5 + 4w) (7(-5 + 4w) + w(-5 + 4w)) = 0 ((-5 * 7 + 4w * 7) + w(-5 + 4w)) = 0 ((-35 + 28w) + w(-5 + 4w)) = 0 (-35 + 28w + (-5 * w + 4w * w)) = 0 (-35 + 28w + (-5w + 4w2)) = 0 Combine like terms: 28w + -5w = 23w (-35 + 23w + 4w2) = 0 Solving -35 + 23w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(5 + -4w) = 0Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 2
Set the factor '(5 + -4w)' equal to zero and attempt to solve: Simplifying 5 + -4w = 0 Solving 5 + -4w = 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 + -4w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4w = 0 + -5 -4w = 0 + -5 Combine like terms: 0 + -5 = -5 -4w = -5 Divide each side by '-4'. w = 1.25 Simplifying w = 1.25Solution
w = {-7, 1.25}
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