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Simplifying -6v + 18 = 6v(v + -3) Reorder the terms: 18 + -6v = 6v(v + -3) Reorder the terms: 18 + -6v = 6v(-3 + v) 18 + -6v = (-3 * 6v + v * 6v) 18 + -6v = (-18v + 6v2) Solving 18 + -6v = -18v + 6v2 Solving for variable 'v'. Combine like terms: -6v + 18v = 12v 18 + 12v + -6v2 = -18v + 6v2 + 18v + -6v2 Reorder the terms: 18 + 12v + -6v2 = -18v + 18v + 6v2 + -6v2 Combine like terms: -18v + 18v = 0 18 + 12v + -6v2 = 0 + 6v2 + -6v2 18 + 12v + -6v2 = 6v2 + -6v2 Combine like terms: 6v2 + -6v2 = 0 18 + 12v + -6v2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(3 + 2v + -1v2) = 0 Factor a trinomial. 6((3 + -1v)(1 + v)) = 0 Ignore the factor 6.Subproblem 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 '(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 = {3, -1}
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