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Simplifying (6v + 4)(9v + 8) = 0 Reorder the terms: (4 + 6v)(9v + 8) = 0 Reorder the terms: (4 + 6v)(8 + 9v) = 0 Multiply (4 + 6v) * (8 + 9v) (4(8 + 9v) + 6v * (8 + 9v)) = 0 ((8 * 4 + 9v * 4) + 6v * (8 + 9v)) = 0 ((32 + 36v) + 6v * (8 + 9v)) = 0 (32 + 36v + (8 * 6v + 9v * 6v)) = 0 (32 + 36v + (48v + 54v2)) = 0 Combine like terms: 36v + 48v = 84v (32 + 84v + 54v2) = 0 Solving 32 + 84v + 54v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(16 + 42v + 27v2) = 0 Factor a trinomial. 2((8 + 9v)(2 + 3v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 9v)' equal to zero and attempt to solve: Simplifying 8 + 9v = 0 Solving 8 + 9v = 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 + 9v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 9v = 0 + -8 9v = 0 + -8 Combine like terms: 0 + -8 = -8 9v = -8 Divide each side by '9'. v = -0.8888888889 Simplifying v = -0.8888888889Subproblem 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 = {-0.8888888889, -0.6666666667}
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