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Simplifying 4w(w + -6)(w + 7) = 0 Reorder the terms: 4w(-6 + w)(w + 7) = 0 Reorder the terms: 4w(-6 + w)(7 + w) = 0 Multiply (-6 + w) * (7 + w) 4w(-6(7 + w) + w(7 + w)) = 0 4w((7 * -6 + w * -6) + w(7 + w)) = 0 4w((-42 + -6w) + w(7 + w)) = 0 4w(-42 + -6w + (7 * w + w * w)) = 0 4w(-42 + -6w + (7w + w2)) = 0 Combine like terms: -6w + 7w = 1w 4w(-42 + 1w + w2) = 0 (-42 * 4w + 1w * 4w + w2 * 4w) = 0 (-168w + 4w2 + 4w3) = 0 Solving -168w + 4w2 + 4w3 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '4w'. 4w(-42 + w + w2) = 0 Factor a trinomial. 4w((-7 + -1w)(6 + -1w)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'w' equal to zero and attempt to solve: Simplifying w = 0 Solving w = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w = 0Subproblem 2
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 3
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 = 6Solution
w = {0, -7, 6}
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