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Simplifying (4w + -7)(3 + w) = 0 Reorder the terms: (-7 + 4w)(3 + w) = 0 Multiply (-7 + 4w) * (3 + w) (-7(3 + w) + 4w * (3 + w)) = 0 ((3 * -7 + w * -7) + 4w * (3 + w)) = 0 ((-21 + -7w) + 4w * (3 + w)) = 0 (-21 + -7w + (3 * 4w + w * 4w)) = 0 (-21 + -7w + (12w + 4w2)) = 0 Combine like terms: -7w + 12w = 5w (-21 + 5w + 4w2) = 0 Solving -21 + 5w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + -1w)(7 + -4w) = 0Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 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 = {-3, 1.75}
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