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Simplifying 4v(7v + -4)(4v + -1) = 0 Reorder the terms: 4v(-4 + 7v)(4v + -1) = 0 Reorder the terms: 4v(-4 + 7v)(-1 + 4v) = 0 Multiply (-4 + 7v) * (-1 + 4v) 4v(-4(-1 + 4v) + 7v * (-1 + 4v)) = 0 4v((-1 * -4 + 4v * -4) + 7v * (-1 + 4v)) = 0 4v((4 + -16v) + 7v * (-1 + 4v)) = 0 4v(4 + -16v + (-1 * 7v + 4v * 7v)) = 0 4v(4 + -16v + (-7v + 28v2)) = 0 Combine like terms: -16v + -7v = -23v 4v(4 + -23v + 28v2) = 0 (4 * 4v + -23v * 4v + 28v2 * 4v) = 0 (16v + -92v2 + 112v3) = 0 Solving 16v + -92v2 + 112v3 = 0 Solving for variable 'v'. Factor out the Greatest Common Factor (GCF), '4v'. 4v(4 + -23v + 28v2) = 0 Factor a trinomial. 4v((1 + -4v)(4 + -7v)) = 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 '(1 + -4v)' equal to zero and attempt to solve: Simplifying 1 + -4v = 0 Solving 1 + -4v = 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 + -4v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -4v = 0 + -1 -4v = 0 + -1 Combine like terms: 0 + -1 = -1 -4v = -1 Divide each side by '-4'. v = 0.25 Simplifying v = 0.25Subproblem 3
Set the factor '(4 + -7v)' equal to zero and attempt to solve: Simplifying 4 + -7v = 0 Solving 4 + -7v = 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 + -7v = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -7v = 0 + -4 -7v = 0 + -4 Combine like terms: 0 + -4 = -4 -7v = -4 Divide each side by '-7'. v = 0.5714285714 Simplifying v = 0.5714285714Solution
v = {0, 0.25, 0.5714285714}
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