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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 = 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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