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Simplifying v2 + 2v + 1 = 2v2 + 8v + 6 Reorder the terms: 1 + 2v + v2 = 2v2 + 8v + 6 Reorder the terms: 1 + 2v + v2 = 6 + 8v + 2v2 Solving 1 + 2v + v2 = 6 + 8v + 2v2 Solving for variable 'v'. Reorder the terms: 1 + -6 + 2v + -8v + v2 + -2v2 = 6 + 8v + 2v2 + -6 + -8v + -2v2 Combine like terms: 1 + -6 = -5 -5 + 2v + -8v + v2 + -2v2 = 6 + 8v + 2v2 + -6 + -8v + -2v2 Combine like terms: 2v + -8v = -6v -5 + -6v + v2 + -2v2 = 6 + 8v + 2v2 + -6 + -8v + -2v2 Combine like terms: v2 + -2v2 = -1v2 -5 + -6v + -1v2 = 6 + 8v + 2v2 + -6 + -8v + -2v2 Reorder the terms: -5 + -6v + -1v2 = 6 + -6 + 8v + -8v + 2v2 + -2v2 Combine like terms: 6 + -6 = 0 -5 + -6v + -1v2 = 0 + 8v + -8v + 2v2 + -2v2 -5 + -6v + -1v2 = 8v + -8v + 2v2 + -2v2 Combine like terms: 8v + -8v = 0 -5 + -6v + -1v2 = 0 + 2v2 + -2v2 -5 + -6v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -5 + -6v + -1v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 6v + v2) = 0 Factor a trinomial. -1((5 + v)(1 + v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + v)' equal to zero and attempt to solve: Simplifying 5 + v = 0 Solving 5 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + v = 0 + -5 v = 0 + -5 Combine like terms: 0 + -5 = -5 v = -5 Simplifying v = -5Subproblem 2
Set the factor '(1 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1Solution
v = {-5, -1}
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