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Simplifying (4 + -1w)(4w + -1) = 0 Reorder the terms: (4 + -1w)(-1 + 4w) = 0 Multiply (4 + -1w) * (-1 + 4w) (4(-1 + 4w) + -1w * (-1 + 4w)) = 0 ((-1 * 4 + 4w * 4) + -1w * (-1 + 4w)) = 0 ((-4 + 16w) + -1w * (-1 + 4w)) = 0 (-4 + 16w + (-1 * -1w + 4w * -1w)) = 0 (-4 + 16w + (1w + -4w2)) = 0 Combine like terms: 16w + 1w = 17w (-4 + 17w + -4w2) = 0 Solving -4 + 17w + -4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-4 + w)(1 + -4w) = 0Subproblem 1
Set the factor '(-4 + w)' equal to zero and attempt to solve: Simplifying -4 + w = 0 Solving -4 + w = 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 + w = 0 + 4 Combine like terms: -4 + 4 = 0 0 + w = 0 + 4 w = 0 + 4 Combine like terms: 0 + 4 = 4 w = 4 Simplifying w = 4Subproblem 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 = {4, 0.25}
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