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Simplifying 6v2 + -12v + -84 = 6 Reorder the terms: -84 + -12v + 6v2 = 6 Solving -84 + -12v + 6v2 = 6 Solving for variable 'v'. Reorder the terms: -84 + -6 + -12v + 6v2 = 6 + -6 Combine like terms: -84 + -6 = -90 -90 + -12v + 6v2 = 6 + -6 Combine like terms: 6 + -6 = 0 -90 + -12v + 6v2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-15 + -2v + v2) = 0 Factor a trinomial. 6((-3 + -1v)(5 + -1v)) = 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 '(5 + -1v)' equal to zero and attempt to solve: Simplifying 5 + -1v = 0 Solving 5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1v = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1v = 0 + -5 -1v = 0 + -5 Combine like terms: 0 + -5 = -5 -1v = -5 Divide each side by '-1'. v = 5 Simplifying v = 5Solution
v = {-3, 5}
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