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Simplifying (8 + v)(4v + 6) = 0 Reorder the terms: (8 + v)(6 + 4v) = 0 Multiply (8 + v) * (6 + 4v) (8(6 + 4v) + v(6 + 4v)) = 0 ((6 * 8 + 4v * 8) + v(6 + 4v)) = 0 ((48 + 32v) + v(6 + 4v)) = 0 (48 + 32v + (6 * v + 4v * v)) = 0 (48 + 32v + (6v + 4v2)) = 0 Combine like terms: 32v + 6v = 38v (48 + 38v + 4v2) = 0 Solving 48 + 38v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 19v + 2v2) = 0 Factor a trinomial. 2((8 + v)(3 + 2v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + v)' equal to zero and attempt to solve: Simplifying 8 + v = 0 Solving 8 + v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + v = 0 + -8 v = 0 + -8 Combine like terms: 0 + -8 = -8 v = -8 Simplifying v = -8Subproblem 2
Set the factor '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 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 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5Solution
v = {-8, -1.5}
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