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Simplifying -4v(v + 6)(v + 7) = 0 Reorder the terms: -4v(6 + v)(v + 7) = 0 Reorder the terms: -4v(6 + v)(7 + v) = 0 Multiply (6 + v) * (7 + v) -4v(6(7 + v) + v(7 + v)) = 0 -4v((7 * 6 + v * 6) + v(7 + v)) = 0 -4v((42 + 6v) + v(7 + v)) = 0 -4v(42 + 6v + (7 * v + v * v)) = 0 -4v(42 + 6v + (7v + v2)) = 0 Combine like terms: 6v + 7v = 13v -4v(42 + 13v + v2) = 0 (42 * -4v + 13v * -4v + v2 * -4v) = 0 (-168v + -52v2 + -4v3) = 0 Solving -168v + -52v2 + -4v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '-4v'. -4v(42 + 13v + v2) = 0 Factor a trinomial. -4v((7 + v)(6 + v)) = 0 Ignore the factor -4.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(7 + v)' equal to zero and attempt to solve: Simplifying 7 + v = 0 Solving 7 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + v = 0 + -7 v = 0 + -7 Combine like terms: 0 + -7 = -7 v = -7 Simplifying v = -7Subproblem 3
Set the factor '(6 + v)' equal to zero and attempt to solve: Simplifying 6 + v = 0 Solving 6 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + v = 0 + -6 v = 0 + -6 Combine like terms: 0 + -6 = -6 v = -6 Simplifying v = -6Solution
v = {0, -7, -6}
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