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Simplifying -7v = v2 + 12 Reorder the terms: -7v = 12 + v2 Solving -7v = 12 + v2 Solving for variable 'v'. Reorder the terms: -12 + -7v + -1v2 = 12 + v2 + -12 + -1v2 Reorder the terms: -12 + -7v + -1v2 = 12 + -12 + v2 + -1v2 Combine like terms: 12 + -12 = 0 -12 + -7v + -1v2 = 0 + v2 + -1v2 -12 + -7v + -1v2 = v2 + -1v2 Combine like terms: v2 + -1v2 = 0 -12 + -7v + -1v2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 7v + v2) = 0 Factor a trinomial. -1((4 + v)(3 + v)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + v)' equal to zero and attempt to solve: Simplifying 4 + v = 0 Solving 4 + v = 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 + v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + v = 0 + -4 v = 0 + -4 Combine like terms: 0 + -4 = -4 v = -4 Simplifying v = -4Subproblem 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 = {-4, -3}
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