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Simplifying 3v(5v + -3)(3v + -1) = 0 Reorder the terms: 3v(-3 + 5v)(3v + -1) = 0 Reorder the terms: 3v(-3 + 5v)(-1 + 3v) = 0 Multiply (-3 + 5v) * (-1 + 3v) 3v(-3(-1 + 3v) + 5v * (-1 + 3v)) = 0 3v((-1 * -3 + 3v * -3) + 5v * (-1 + 3v)) = 0 3v((3 + -9v) + 5v * (-1 + 3v)) = 0 3v(3 + -9v + (-1 * 5v + 3v * 5v)) = 0 3v(3 + -9v + (-5v + 15v2)) = 0 Combine like terms: -9v + -5v = -14v 3v(3 + -14v + 15v2) = 0 (3 * 3v + -14v * 3v + 15v2 * 3v) = 0 (9v + -42v2 + 45v3) = 0 Solving 9v + -42v2 + 45v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '3v'. 3v(3 + -14v + 15v2) = 0 Factor a trinomial. 3v((1 + -3v)(3 + -5v)) = 0 Ignore the factor 3.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 '(1 + -3v)' equal to zero and attempt to solve: Simplifying 1 + -3v = 0 Solving 1 + -3v = 0 Move all terms containing v to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3v = 0 + -1 -3v = 0 + -1 Combine like terms: 0 + -1 = -1 -3v = -1 Divide each side by '-3'. v = 0.3333333333 Simplifying v = 0.3333333333Subproblem 3
Set the factor '(3 + -5v)' equal to zero and attempt to solve: Simplifying 3 + -5v = 0 Solving 3 + -5v = 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 + -5v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5v = 0 + -3 -5v = 0 + -3 Combine like terms: 0 + -3 = -3 -5v = -3 Divide each side by '-5'. v = 0.6 Simplifying v = 0.6Solution
v = {0, 0.3333333333, 0.6}
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