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Simplifying 16v + 12v2 = 4v(4 + a) 16v + 12v2 = (4 * 4v + a * 4v) Reorder the terms: 16v + 12v2 = (4av + 16v) 16v + 12v2 = (4av + 16v) Add '-16v' to each side of the equation. 16v + -16v + 12v2 = 4av + 16v + -16v Combine like terms: 16v + -16v = 0 0 + 12v2 = 4av + 16v + -16v 12v2 = 4av + 16v + -16v Combine like terms: 16v + -16v = 0 12v2 = 4av + 0 12v2 = 4av Solving 12v2 = 4av Solving for variable 'v'. Reorder the terms: -4av + 12v2 = 4av + -4av Combine like terms: 4av + -4av = 0 -4av + 12v2 = 0 Factor out the Greatest Common Factor (GCF), '4v'. 4v(-1a + 3v) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v' equal to zero and attempt to solve: Simplifying v = 0 Solving v = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v = 0Subproblem 2
Set the factor '(-1a + 3v)' equal to zero and attempt to solve: Simplifying -1a + 3v = 0 Solving -1a + 3v = 0 Move all terms containing v to the left, all other terms to the right. Add 'a' to each side of the equation. -1a + a + 3v = 0 + a Combine like terms: -1a + a = 0 0 + 3v = 0 + a 3v = 0 + a Remove the zero: 3v = a Divide each side by '3'. v = 0.3333333333a Simplifying v = 0.3333333333aSolution
v = {0, 0.3333333333a}
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