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Simplifying (4 + w)(4w + -2) = 0 Reorder the terms: (4 + w)(-2 + 4w) = 0 Multiply (4 + w) * (-2 + 4w) (4(-2 + 4w) + w(-2 + 4w)) = 0 ((-2 * 4 + 4w * 4) + w(-2 + 4w)) = 0 ((-8 + 16w) + w(-2 + 4w)) = 0 (-8 + 16w + (-2 * w + 4w * w)) = 0 (-8 + 16w + (-2w + 4w2)) = 0 Combine like terms: 16w + -2w = 14w (-8 + 14w + 4w2) = 0 Solving -8 + 14w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + 7w + 2w2) = 0 Factor a trinomial. 2((-4 + -1w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 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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