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Simplifying (8v + 4)(6v + 3) = 0 Reorder the terms: (4 + 8v)(6v + 3) = 0 Reorder the terms: (4 + 8v)(3 + 6v) = 0 Multiply (4 + 8v) * (3 + 6v) (4(3 + 6v) + 8v * (3 + 6v)) = 0 ((3 * 4 + 6v * 4) + 8v * (3 + 6v)) = 0 ((12 + 24v) + 8v * (3 + 6v)) = 0 (12 + 24v + (3 * 8v + 6v * 8v)) = 0 (12 + 24v + (24v + 48v2)) = 0 Combine like terms: 24v + 24v = 48v (12 + 48v + 48v2) = 0 Solving 12 + 48v + 48v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '12'. 12(1 + 4v + 4v2) = 0 Factor a trinomial. 12((1 + 2v)(1 + 2v)) = 0 Ignore the factor 12.Subproblem 1
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 = -0.5Subproblem 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 = {-0.5, -0.5}
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