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Simplifying (5 + -1w)(4w + 1) = 0 Reorder the terms: (5 + -1w)(1 + 4w) = 0 Multiply (5 + -1w) * (1 + 4w) (5(1 + 4w) + -1w * (1 + 4w)) = 0 ((1 * 5 + 4w * 5) + -1w * (1 + 4w)) = 0 ((5 + 20w) + -1w * (1 + 4w)) = 0 (5 + 20w + (1 * -1w + 4w * -1w)) = 0 (5 + 20w + (-1w + -4w2)) = 0 Combine like terms: 20w + -1w = 19w (5 + 19w + -4w2) = 0 Solving 5 + 19w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (5 + -1w)(1 + 4w) = 0Subproblem 1
Set the factor '(5 + -1w)' equal to zero and attempt to solve: Simplifying 5 + -1w = 0 Solving 5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1w = 0 + -5 -1w = 0 + -5 Combine like terms: 0 + -5 = -5 -1w = -5 Divide each side by '-1'. w = 5 Simplifying w = 5Subproblem 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 = {5, -0.25}
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