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Simplifying v2 + 12v + 36 = 2v2 + 14v + 33 Reorder the terms: 36 + 12v + v2 = 2v2 + 14v + 33 Reorder the terms: 36 + 12v + v2 = 33 + 14v + 2v2 Solving 36 + 12v + v2 = 33 + 14v + 2v2 Solving for variable 'v'. Reorder the terms: 36 + -33 + 12v + -14v + v2 + -2v2 = 33 + 14v + 2v2 + -33 + -14v + -2v2 Combine like terms: 36 + -33 = 3 3 + 12v + -14v + v2 + -2v2 = 33 + 14v + 2v2 + -33 + -14v + -2v2 Combine like terms: 12v + -14v = -2v 3 + -2v + v2 + -2v2 = 33 + 14v + 2v2 + -33 + -14v + -2v2 Combine like terms: v2 + -2v2 = -1v2 3 + -2v + -1v2 = 33 + 14v + 2v2 + -33 + -14v + -2v2 Reorder the terms: 3 + -2v + -1v2 = 33 + -33 + 14v + -14v + 2v2 + -2v2 Combine like terms: 33 + -33 = 0 3 + -2v + -1v2 = 0 + 14v + -14v + 2v2 + -2v2 3 + -2v + -1v2 = 14v + -14v + 2v2 + -2v2 Combine like terms: 14v + -14v = 0 3 + -2v + -1v2 = 0 + 2v2 + -2v2 3 + -2v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 3 + -2v + -1v2 = 0 Factor a trinomial. (1 + -1v)(3 + v) = 0Subproblem 1
Set the factor '(1 + -1v)' equal to zero and attempt to solve: Simplifying 1 + -1v = 0 Solving 1 + -1v = 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 + -1v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1v = 0 + -1 -1v = 0 + -1 Combine like terms: 0 + -1 = -1 -1v = -1 Divide each side by '-1'. v = 1 Simplifying v = 1Subproblem 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 = {1, -3}
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