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Simplifying -2v2 + -1v + 12 = -3v2 + 6v Reorder the terms: 12 + -1v + -2v2 = -3v2 + 6v Reorder the terms: 12 + -1v + -2v2 = 6v + -3v2 Solving 12 + -1v + -2v2 = 6v + -3v2 Solving for variable 'v'. Reorder the terms: 12 + -1v + -6v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2 Combine like terms: -1v + -6v = -7v 12 + -7v + -2v2 + 3v2 = 6v + -3v2 + -6v + 3v2 Combine like terms: -2v2 + 3v2 = 1v2 12 + -7v + 1v2 = 6v + -3v2 + -6v + 3v2 Reorder the terms: 12 + -7v + 1v2 = 6v + -6v + -3v2 + 3v2 Combine like terms: 6v + -6v = 0 12 + -7v + 1v2 = 0 + -3v2 + 3v2 12 + -7v + 1v2 = -3v2 + 3v2 Combine like terms: -3v2 + 3v2 = 0 12 + -7v + 1v2 = 0 Factor a trinomial. (3 + -1v)(4 + -1v) = 0Subproblem 1
Set the factor '(3 + -1v)' equal to zero and attempt to solve: Simplifying 3 + -1v = 0 Solving 3 + -1v = 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 + -1v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1v = 0 + -3 -1v = 0 + -3 Combine like terms: 0 + -3 = -3 -1v = -3 Divide each side by '-1'. v = 3 Simplifying v = 3Subproblem 2
Set the factor '(4 + -1v)' equal to zero and attempt to solve: Simplifying 4 + -1v = 0 Solving 4 + -1v = 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 + -1v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1v = 0 + -4 -1v = 0 + -4 Combine like terms: 0 + -4 = -4 -1v = -4 Divide each side by '-1'. v = 4 Simplifying v = 4Solution
v = {3, 4}
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