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Simplifying (2 + -1w)(4w + 1) = 0 Reorder the terms: (2 + -1w)(1 + 4w) = 0 Multiply (2 + -1w) * (1 + 4w) (2(1 + 4w) + -1w * (1 + 4w)) = 0 ((1 * 2 + 4w * 2) + -1w * (1 + 4w)) = 0 ((2 + 8w) + -1w * (1 + 4w)) = 0 (2 + 8w + (1 * -1w + 4w * -1w)) = 0 (2 + 8w + (-1w + -4w2)) = 0 Combine like terms: 8w + -1w = 7w (2 + 7w + -4w2) = 0 Solving 2 + 7w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (2 + -1w)(1 + 4w) = 0Subproblem 1
Set the factor '(2 + -1w)' equal to zero and attempt to solve: Simplifying 2 + -1w = 0 Solving 2 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1w = 0 + -2 -1w = 0 + -2 Combine like terms: 0 + -2 = -2 -1w = -2 Divide each side by '-1'. w = 2 Simplifying w = 2Subproblem 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 = {2, -0.25}
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