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Simplifying (3v + -4)(4v + -6) = 0 Reorder the terms: (-4 + 3v)(4v + -6) = 0 Reorder the terms: (-4 + 3v)(-6 + 4v) = 0 Multiply (-4 + 3v) * (-6 + 4v) (-4(-6 + 4v) + 3v * (-6 + 4v)) = 0 ((-6 * -4 + 4v * -4) + 3v * (-6 + 4v)) = 0 ((24 + -16v) + 3v * (-6 + 4v)) = 0 (24 + -16v + (-6 * 3v + 4v * 3v)) = 0 (24 + -16v + (-18v + 12v2)) = 0 Combine like terms: -16v + -18v = -34v (24 + -34v + 12v2) = 0 Solving 24 + -34v + 12v2 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -17v + 6v2) = 0 Factor a trinomial. 2((4 + -3v)(3 + -2v)) = 0 Ignore the factor 2.Subproblem 1
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 = 1.333333333Subproblem 2
Set the factor '(3 + -2v)' equal to zero and attempt to solve: Simplifying 3 + -2v = 0 Solving 3 + -2v = 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 + -2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2v = 0 + -3 -2v = 0 + -3 Combine like terms: 0 + -3 = -3 -2v = -3 Divide each side by '-2'. v = 1.5 Simplifying v = 1.5Solution
v = {1.333333333, 1.5}
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