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Simplifying (7 + -1w)(4w + 3) = 0 Reorder the terms: (7 + -1w)(3 + 4w) = 0 Multiply (7 + -1w) * (3 + 4w) (7(3 + 4w) + -1w * (3 + 4w)) = 0 ((3 * 7 + 4w * 7) + -1w * (3 + 4w)) = 0 ((21 + 28w) + -1w * (3 + 4w)) = 0 (21 + 28w + (3 * -1w + 4w * -1w)) = 0 (21 + 28w + (-3w + -4w2)) = 0 Combine like terms: 28w + -3w = 25w (21 + 25w + -4w2) = 0 Solving 21 + 25w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + -1w)(3 + 4w) = 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 '(3 + 4w)' equal to zero and attempt to solve: Simplifying 3 + 4w = 0 Solving 3 + 4w = 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 + 4w = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4w = 0 + -3 4w = 0 + -3 Combine like terms: 0 + -3 = -3 4w = -3 Divide each side by '4'. w = -0.75 Simplifying w = -0.75Solution
w = {7, -0.75}
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