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Simplifying v2 + -6v + 9 = 2v2 + 2v + 21 Reorder the terms: 9 + -6v + v2 = 2v2 + 2v + 21 Reorder the terms: 9 + -6v + v2 = 21 + 2v + 2v2 Solving 9 + -6v + v2 = 21 + 2v + 2v2 Solving for variable 'v'. Reorder the terms: 9 + -21 + -6v + -2v + v2 + -2v2 = 21 + 2v + 2v2 + -21 + -2v + -2v2 Combine like terms: 9 + -21 = -12 -12 + -6v + -2v + v2 + -2v2 = 21 + 2v + 2v2 + -21 + -2v + -2v2 Combine like terms: -6v + -2v = -8v -12 + -8v + v2 + -2v2 = 21 + 2v + 2v2 + -21 + -2v + -2v2 Combine like terms: v2 + -2v2 = -1v2 -12 + -8v + -1v2 = 21 + 2v + 2v2 + -21 + -2v + -2v2 Reorder the terms: -12 + -8v + -1v2 = 21 + -21 + 2v + -2v + 2v2 + -2v2 Combine like terms: 21 + -21 = 0 -12 + -8v + -1v2 = 0 + 2v + -2v + 2v2 + -2v2 -12 + -8v + -1v2 = 2v + -2v + 2v2 + -2v2 Combine like terms: 2v + -2v = 0 -12 + -8v + -1v2 = 0 + 2v2 + -2v2 -12 + -8v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -12 + -8v + -1v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 8v + v2) = 0 Factor a trinomial. -1((6 + v)(2 + v)) = 0 Ignore the factor -1.Subproblem 1
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 2
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 = {-6, -2}
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