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Simplifying 0 = v2 + 12v + 27 Reorder the terms: 0 = 27 + 12v + v2 Solving 0 = 27 + 12v + v2 Solving for variable 'v'. Combine like terms: 0 + -27 = -27 -27 + -12v + -1v2 = 27 + 12v + v2 + -27 + -12v + -1v2 Reorder the terms: -27 + -12v + -1v2 = 27 + -27 + 12v + -12v + v2 + -1v2 Combine like terms: 27 + -27 = 0 -27 + -12v + -1v2 = 0 + 12v + -12v + v2 + -1v2 -27 + -12v + -1v2 = 12v + -12v + v2 + -1v2 Combine like terms: 12v + -12v = 0 -27 + -12v + -1v2 = 0 + v2 + -1v2 -27 + -12v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -27 + -12v + -1v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(27 + 12v + v2) = 0 Factor a trinomial. -1((9 + v)(3 + v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + v)' equal to zero and attempt to solve: Simplifying 9 + v = 0 Solving 9 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + v = 0 + -9 v = 0 + -9 Combine like terms: 0 + -9 = -9 v = -9 Simplifying v = -9Subproblem 2
Set the factor '(3 + v)' equal to zero and attempt to solve: Simplifying 3 + v = 0 Solving 3 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + v = 0 + -3 v = 0 + -3 Combine like terms: 0 + -3 = -3 v = -3 Simplifying v = -3Solution
v = {-9, -3}
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