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Simplifying (4w + -4)(w + 6) = 0 Reorder the terms: (-4 + 4w)(w + 6) = 0 Reorder the terms: (-4 + 4w)(6 + w) = 0 Multiply (-4 + 4w) * (6 + w) (-4(6 + w) + 4w * (6 + w)) = 0 ((6 * -4 + w * -4) + 4w * (6 + w)) = 0 ((-24 + -4w) + 4w * (6 + w)) = 0 (-24 + -4w + (6 * 4w + w * 4w)) = 0 (-24 + -4w + (24w + 4w2)) = 0 Combine like terms: -4w + 24w = 20w (-24 + 20w + 4w2) = 0 Solving -24 + 20w + 4w2 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4'. 4(-6 + 5w + w2) = 0 Factor a trinomial. 4((-6 + -1w)(1 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6Subproblem 2
Set the factor '(1 + -1w)' equal to zero and attempt to solve: Simplifying 1 + -1w = 0 Solving 1 + -1w = 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 + -1w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1w = 0 + -1 -1w = 0 + -1 Combine like terms: 0 + -1 = -1 -1w = -1 Divide each side by '-1'. w = 1 Simplifying w = 1Solution
w = {-6, 1}
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