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Simplifying (4w + -7)(2 + -1w) = 0 Reorder the terms: (-7 + 4w)(2 + -1w) = 0 Multiply (-7 + 4w) * (2 + -1w) (-7(2 + -1w) + 4w * (2 + -1w)) = 0 ((2 * -7 + -1w * -7) + 4w * (2 + -1w)) = 0 ((-14 + 7w) + 4w * (2 + -1w)) = 0 (-14 + 7w + (2 * 4w + -1w * 4w)) = 0 (-14 + 7w + (8w + -4w2)) = 0 Combine like terms: 7w + 8w = 15w (-14 + 15w + -4w2) = 0 Solving -14 + 15w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-2 + w)(7 + -4w) = 0Subproblem 1
Set the factor '(-2 + w)' equal to zero and attempt to solve: Simplifying -2 + w = 0 Solving -2 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + w = 0 + 2 Combine like terms: -2 + 2 = 0 0 + w = 0 + 2 w = 0 + 2 Combine like terms: 0 + 2 = 2 w = 2 Simplifying w = 2Subproblem 2
Set the factor '(7 + -4w)' equal to zero and attempt to solve: Simplifying 7 + -4w = 0 Solving 7 + -4w = 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 + -4w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4w = 0 + -7 -4w = 0 + -7 Combine like terms: 0 + -7 = -7 -4w = -7 Divide each side by '-4'. w = 1.75 Simplifying w = 1.75Solution
w = {2, 1.75}
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