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Simplifying 4v3 + -8v2 = 140v Reorder the terms: -8v2 + 4v3 = 140v Solving -8v2 + 4v3 = 140v Solving for variable 'v'. Reorder the terms: -140v + -8v2 + 4v3 = 140v + -140v Combine like terms: 140v + -140v = 0 -140v + -8v2 + 4v3 = 0 Factor out the Greatest Common Factor (GCF), '4v'. 4v(-35 + -2v + v2) = 0 Factor a trinomial. 4v((-5 + -1v)(7 + -1v)) = 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 '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5Subproblem 3
Set the factor '(7 + -1v)' equal to zero and attempt to solve: Simplifying 7 + -1v = 0 Solving 7 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1v = 0 + -7 -1v = 0 + -7 Combine like terms: 0 + -7 = -7 -1v = -7 Divide each side by '-1'. v = 7 Simplifying v = 7Solution
v = {0, -5, 7}
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