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Simplifying (3 + -1w)(4w + -7) = 0 Reorder the terms: (3 + -1w)(-7 + 4w) = 0 Multiply (3 + -1w) * (-7 + 4w) (3(-7 + 4w) + -1w * (-7 + 4w)) = 0 ((-7 * 3 + 4w * 3) + -1w * (-7 + 4w)) = 0 ((-21 + 12w) + -1w * (-7 + 4w)) = 0 (-21 + 12w + (-7 * -1w + 4w * -1w)) = 0 (-21 + 12w + (7w + -4w2)) = 0 Combine like terms: 12w + 7w = 19w (-21 + 19w + -4w2) = 0 Solving -21 + 19w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-3 + w)(7 + -4w) = 0Subproblem 1
Set the factor '(-3 + w)' equal to zero and attempt to solve: Simplifying -3 + w = 0 Solving -3 + w = 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 + w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + w = 0 + 3 w = 0 + 3 Combine like terms: 0 + 3 = 3 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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