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Simplifying (4 + -1w)(2w + 1) = 0 Reorder the terms: (4 + -1w)(1 + 2w) = 0 Multiply (4 + -1w) * (1 + 2w) (4(1 + 2w) + -1w * (1 + 2w)) = 0 ((1 * 4 + 2w * 4) + -1w * (1 + 2w)) = 0 ((4 + 8w) + -1w * (1 + 2w)) = 0 (4 + 8w + (1 * -1w + 2w * -1w)) = 0 (4 + 8w + (-1w + -2w2)) = 0 Combine like terms: 8w + -1w = 7w (4 + 7w + -2w2) = 0 Solving 4 + 7w + -2w2 = 0 Solving for variable 'w'. Factor a trinomial. (4 + -1w)(1 + 2w) = 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 '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 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 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5Solution
w = {4, -0.5}
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