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Simplifying (8v + 7)(9v + 6) = 0 Reorder the terms: (7 + 8v)(9v + 6) = 0 Reorder the terms: (7 + 8v)(6 + 9v) = 0 Multiply (7 + 8v) * (6 + 9v) (7(6 + 9v) + 8v * (6 + 9v)) = 0 ((6 * 7 + 9v * 7) + 8v * (6 + 9v)) = 0 ((42 + 63v) + 8v * (6 + 9v)) = 0 (42 + 63v + (6 * 8v + 9v * 8v)) = 0 (42 + 63v + (48v + 72v2)) = 0 Combine like terms: 63v + 48v = 111v (42 + 111v + 72v2) = 0 Solving 42 + 111v + 72v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3'. 3(14 + 37v + 24v2) = 0 Factor a trinomial. 3((7 + 8v)(2 + 3v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 8v)' equal to zero and attempt to solve: Simplifying 7 + 8v = 0 Solving 7 + 8v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 8v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 8v = 0 + -7 8v = 0 + -7 Combine like terms: 0 + -7 = -7 8v = -7 Divide each side by '8'. v = -0.875 Simplifying v = -0.875Subproblem 2
Set the factor '(2 + 3v)' equal to zero and attempt to solve: Simplifying 2 + 3v = 0 Solving 2 + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3v = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3v = 0 + -2 3v = 0 + -2 Combine like terms: 0 + -2 = -2 3v = -2 Divide each side by '3'. v = -0.6666666667 Simplifying v = -0.6666666667Solution
v = {-0.875, -0.6666666667}
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