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Simplifying (4w + 1)(7 + w) = 0 Reorder the terms: (1 + 4w)(7 + w) = 0 Multiply (1 + 4w) * (7 + w) (1(7 + w) + 4w * (7 + w)) = 0 ((7 * 1 + w * 1) + 4w * (7 + w)) = 0 ((7 + 1w) + 4w * (7 + w)) = 0 (7 + 1w + (7 * 4w + w * 4w)) = 0 (7 + 1w + (28w + 4w2)) = 0 Combine like terms: 1w + 28w = 29w (7 + 29w + 4w2) = 0 Solving 7 + 29w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + w)(1 + 4w) = 0Subproblem 1
Set the factor '(7 + w)' equal to zero and attempt to solve: Simplifying 7 + w = 0 Solving 7 + w = 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 + w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + w = 0 + -7 w = 0 + -7 Combine like terms: 0 + -7 = -7 w = -7 Simplifying w = -7Subproblem 2
Set the factor '(1 + 4w)' equal to zero and attempt to solve: Simplifying 1 + 4w = 0 Solving 1 + 4w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 4w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4w = 0 + -1 4w = 0 + -1 Combine like terms: 0 + -1 = -1 4w = -1 Divide each side by '4'. w = -0.25 Simplifying w = -0.25Solution
w = {-7, -0.25}
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