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Simplifying (8v + -6)(3v + -4) = 0 Reorder the terms: (-6 + 8v)(3v + -4) = 0 Reorder the terms: (-6 + 8v)(-4 + 3v) = 0 Multiply (-6 + 8v) * (-4 + 3v) (-6(-4 + 3v) + 8v * (-4 + 3v)) = 0 ((-4 * -6 + 3v * -6) + 8v * (-4 + 3v)) = 0 ((24 + -18v) + 8v * (-4 + 3v)) = 0 (24 + -18v + (-4 * 8v + 3v * 8v)) = 0 (24 + -18v + (-32v + 24v2)) = 0 Combine like terms: -18v + -32v = -50v (24 + -50v + 24v2) = 0 Solving 24 + -50v + 24v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -25v + 12v2) = 0 Factor a trinomial. 2((3 + -4v)(4 + -3v)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.75Subproblem 2
Set the factor '(4 + -3v)' equal to zero and attempt to solve: Simplifying 4 + -3v = 0 Solving 4 + -3v = 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 + -3v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3v = 0 + -4 -3v = 0 + -4 Combine like terms: 0 + -4 = -4 -3v = -4 Divide each side by '-3'. v = 1.333333333 Simplifying v = 1.333333333Solution
v = {0.75, 1.333333333}
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