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Simplifying (v + -3)(v + -3) = 2v2 + -9v + -9 Reorder the terms: (-3 + v)(v + -3) = 2v2 + -9v + -9 Reorder the terms: (-3 + v)(-3 + v) = 2v2 + -9v + -9 Multiply (-3 + v) * (-3 + v) (-3(-3 + v) + v(-3 + v)) = 2v2 + -9v + -9 ((-3 * -3 + v * -3) + v(-3 + v)) = 2v2 + -9v + -9 ((9 + -3v) + v(-3 + v)) = 2v2 + -9v + -9 (9 + -3v + (-3 * v + v * v)) = 2v2 + -9v + -9 (9 + -3v + (-3v + v2)) = 2v2 + -9v + -9 Combine like terms: -3v + -3v = -6v (9 + -6v + v2) = 2v2 + -9v + -9 Reorder the terms: 9 + -6v + v2 = -9 + -9v + 2v2 Solving 9 + -6v + v2 = -9 + -9v + 2v2 Solving for variable 'v'. Reorder the terms: 9 + 9 + -6v + 9v + v2 + -2v2 = -9 + -9v + 2v2 + 9 + 9v + -2v2 Combine like terms: 9 + 9 = 18 18 + -6v + 9v + v2 + -2v2 = -9 + -9v + 2v2 + 9 + 9v + -2v2 Combine like terms: -6v + 9v = 3v 18 + 3v + v2 + -2v2 = -9 + -9v + 2v2 + 9 + 9v + -2v2 Combine like terms: v2 + -2v2 = -1v2 18 + 3v + -1v2 = -9 + -9v + 2v2 + 9 + 9v + -2v2 Reorder the terms: 18 + 3v + -1v2 = -9 + 9 + -9v + 9v + 2v2 + -2v2 Combine like terms: -9 + 9 = 0 18 + 3v + -1v2 = 0 + -9v + 9v + 2v2 + -2v2 18 + 3v + -1v2 = -9v + 9v + 2v2 + -2v2 Combine like terms: -9v + 9v = 0 18 + 3v + -1v2 = 0 + 2v2 + -2v2 18 + 3v + -1v2 = 2v2 + -2v2 Combine like terms: 2v2 + -2v2 = 0 18 + 3v + -1v2 = 0 Factor a trinomial. (6 + -1v)(3 + v) = 0Subproblem 1
Set the factor '(6 + -1v)' equal to zero and attempt to solve: Simplifying 6 + -1v = 0 Solving 6 + -1v = 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 + -1v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1v = 0 + -6 -1v = 0 + -6 Combine like terms: 0 + -6 = -6 -1v = -6 Divide each side by '-1'. v = 6 Simplifying v = 6Subproblem 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 = {6, -3}
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