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Simplifying (7 + w)(4w + -2) = 0 Reorder the terms: (7 + w)(-2 + 4w) = 0 Multiply (7 + w) * (-2 + 4w) (7(-2 + 4w) + w(-2 + 4w)) = 0 ((-2 * 7 + 4w * 7) + w(-2 + 4w)) = 0 ((-14 + 28w) + w(-2 + 4w)) = 0 (-14 + 28w + (-2 * w + 4w * w)) = 0 (-14 + 28w + (-2w + 4w2)) = 0 Combine like terms: 28w + -2w = 26w (-14 + 26w + 4w2) = 0 Solving -14 + 26w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 13w + 2w2) = 0 Factor a trinomial. 2((-7 + -1w)(1 + -2w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7Subproblem 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 = {-7, 0.5}
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