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Simplifying (4 + -1w)(4w + 7) = 0 Reorder the terms: (4 + -1w)(7 + 4w) = 0 Multiply (4 + -1w) * (7 + 4w) (4(7 + 4w) + -1w * (7 + 4w)) = 0 ((7 * 4 + 4w * 4) + -1w * (7 + 4w)) = 0 ((28 + 16w) + -1w * (7 + 4w)) = 0 (28 + 16w + (7 * -1w + 4w * -1w)) = 0 (28 + 16w + (-7w + -4w2)) = 0 Combine like terms: 16w + -7w = 9w (28 + 9w + -4w2) = 0 Solving 28 + 9w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + -1w)(7 + 4w) = 0Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4Subproblem 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 = {4, -1.75}
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