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Simplifying (4 + v)(4v + 2) = 0 Reorder the terms: (4 + v)(2 + 4v) = 0 Multiply (4 + v) * (2 + 4v) (4(2 + 4v) + v(2 + 4v)) = 0 ((2 * 4 + 4v * 4) + v(2 + 4v)) = 0 ((8 + 16v) + v(2 + 4v)) = 0 (8 + 16v + (2 * v + 4v * v)) = 0 (8 + 16v + (2v + 4v2)) = 0 Combine like terms: 16v + 2v = 18v (8 + 18v + 4v2) = 0 Solving 8 + 18v + 4v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 9v + 2v2) = 0 Factor a trinomial. 2((4 + v)(1 + 2v)) = 0 Ignore the factor 2.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 '(1 + 2v)' equal to zero and attempt to solve: Simplifying 1 + 2v = 0 Solving 1 + 2v = 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 + 2v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2v = 0 + -1 2v = 0 + -1 Combine like terms: 0 + -1 = -1 2v = -1 Divide each side by '2'. v = -0.5 Simplifying v = -0.5Solution
v = {-4, -0.5}
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