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Simplifying (7 + w)(3w + -4) = 0 Reorder the terms: (7 + w)(-4 + 3w) = 0 Multiply (7 + w) * (-4 + 3w) (7(-4 + 3w) + w(-4 + 3w)) = 0 ((-4 * 7 + 3w * 7) + w(-4 + 3w)) = 0 ((-28 + 21w) + w(-4 + 3w)) = 0 (-28 + 21w + (-4 * w + 3w * w)) = 0 (-28 + 21w + (-4w + 3w2)) = 0 Combine like terms: 21w + -4w = 17w (-28 + 17w + 3w2) = 0 Solving -28 + 17w + 3w2 = 0 Solving for variable 'w'. Factor a trinomial. (-7 + -1w)(4 + -3w) = 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 '(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 = {-7, 1.333333333}
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