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Simplifying 4v(v + 6)(v + 2) = 0 Reorder the terms: 4v(6 + v)(v + 2) = 0 Reorder the terms: 4v(6 + v)(2 + v) = 0 Multiply (6 + v) * (2 + v) 4v(6(2 + v) + v(2 + v)) = 0 4v((2 * 6 + v * 6) + v(2 + v)) = 0 4v((12 + 6v) + v(2 + v)) = 0 4v(12 + 6v + (2 * v + v * v)) = 0 4v(12 + 6v + (2v + v2)) = 0 Combine like terms: 6v + 2v = 8v 4v(12 + 8v + v2) = 0 (12 * 4v + 8v * 4v + v2 * 4v) = 0 (48v + 32v2 + 4v3) = 0 Solving 48v + 32v2 + 4v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v'. 4v(12 + 8v + v2) = 0 Factor a trinomial. 4v((6 + v)(2 + 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 '(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 = -6Subproblem 3
Set the factor '(2 + v)' equal to zero and attempt to solve: Simplifying 2 + v = 0 Solving 2 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + v = 0 + -2 v = 0 + -2 Combine like terms: 0 + -2 = -2 v = -2 Simplifying v = -2Solution
v = {0, -6, -2}
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