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Simplifying 6v(5v + -6)(6v + -1) = 0 Reorder the terms: 6v(-6 + 5v)(6v + -1) = 0 Reorder the terms: 6v(-6 + 5v)(-1 + 6v) = 0 Multiply (-6 + 5v) * (-1 + 6v) 6v(-6(-1 + 6v) + 5v * (-1 + 6v)) = 0 6v((-1 * -6 + 6v * -6) + 5v * (-1 + 6v)) = 0 6v((6 + -36v) + 5v * (-1 + 6v)) = 0 6v(6 + -36v + (-1 * 5v + 6v * 5v)) = 0 6v(6 + -36v + (-5v + 30v2)) = 0 Combine like terms: -36v + -5v = -41v 6v(6 + -41v + 30v2) = 0 (6 * 6v + -41v * 6v + 30v2 * 6v) = 0 (36v + -246v2 + 180v3) = 0 Solving 36v + -246v2 + 180v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '6v'. 6v(6 + -41v + 30v2) = 0 Factor a trinomial. 6v((1 + -6v)(6 + -5v)) = 0 Ignore the factor 6.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 + -6v)' equal to zero and attempt to solve: Simplifying 1 + -6v = 0 Solving 1 + -6v = 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 + -6v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6v = 0 + -1 -6v = 0 + -1 Combine like terms: 0 + -1 = -1 -6v = -1 Divide each side by '-6'. v = 0.1666666667 Simplifying v = 0.1666666667Subproblem 3
Set the factor '(6 + -5v)' equal to zero and attempt to solve: Simplifying 6 + -5v = 0 Solving 6 + -5v = 0 Move all terms containing v to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5v = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5v = 0 + -6 -5v = 0 + -6 Combine like terms: 0 + -6 = -6 -5v = -6 Divide each side by '-5'. v = 1.2 Simplifying v = 1.2Solution
v = {0, 0.1666666667, 1.2}
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