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Simplifying v2 + -12v + 36 = 2v2 + -1v + 64 Reorder the terms: 36 + -12v + v2 = 2v2 + -1v + 64 Reorder the terms: 36 + -12v + v2 = 64 + -1v + 2v2 Solving 36 + -12v + v2 = 64 + -1v + 2v2 Solving for variable 'v'. Reorder the terms: 36 + -64 + -12v + v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2 Combine like terms: 36 + -64 = -28 -28 + -12v + v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2 Combine like terms: -12v + v = -11v -28 + -11v + v2 + -2v2 = 64 + -1v + 2v2 + -64 + v + -2v2 Combine like terms: v2 + -2v2 = -1v2 -28 + -11v + -1v2 = 64 + -1v + 2v2 + -64 + v + -2v2 Reorder the terms: -28 + -11v + -1v2 = 64 + -64 + -1v + v + 2v2 + -2v2 Combine like terms: 64 + -64 = 0 -28 + -11v + -1v2 = 0 + -1v + v + 2v2 + -2v2 -28 + -11v + -1v2 = -1v + v + 2v2 + -2v2 Combine like terms: -1v + v = 0 -28 + -11v + -1v2 = 0 + 2v2 + -2v2 -28 + -11v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 -28 + -11v + -1v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(28 + 11v + v2) = 0 Factor a trinomial. -1((7 + v)(4 + v)) = 0 Ignore the factor -1.Subproblem 1
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 2
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Solution
v = {-7, -4}
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