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Simplifying (8v + 6)(4v + 9) = 0 Reorder the terms: (6 + 8v)(4v + 9) = 0 Reorder the terms: (6 + 8v)(9 + 4v) = 0 Multiply (6 + 8v) * (9 + 4v) (6(9 + 4v) + 8v * (9 + 4v)) = 0 ((9 * 6 + 4v * 6) + 8v * (9 + 4v)) = 0 ((54 + 24v) + 8v * (9 + 4v)) = 0 (54 + 24v + (9 * 8v + 4v * 8v)) = 0 (54 + 24v + (72v + 32v2)) = 0 Combine like terms: 24v + 72v = 96v (54 + 96v + 32v2) = 0 Solving 54 + 96v + 32v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 48v + 16v2) = 0 Factor a trinomial. 2((9 + 4v)(3 + 4v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + 4v)' equal to zero and attempt to solve: Simplifying 9 + 4v = 0 Solving 9 + 4v = 0 Move all terms containing v to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 4v = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 4v = 0 + -9 4v = 0 + -9 Combine like terms: 0 + -9 = -9 4v = -9 Divide each side by '4'. v = -2.25 Simplifying v = -2.25Subproblem 2
Set the factor '(3 + 4v)' equal to zero and attempt to solve: Simplifying 3 + 4v = 0 Solving 3 + 4v = 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 + 4v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4v = 0 + -3 4v = 0 + -3 Combine like terms: 0 + -3 = -3 4v = -3 Divide each side by '4'. v = -0.75 Simplifying v = -0.75Solution
v = {-2.25, -0.75}
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