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Simplifying 0 = 12v5 + -16v4 + -28v3 Reorder the terms: 0 = -28v3 + -16v4 + 12v5 Solving 0 = -28v3 + -16v4 + 12v5 Solving for variable 'v'. Remove the zero: 28v3 + 16v4 + -12v5 = -28v3 + -16v4 + 12v5 + 28v3 + 16v4 + -12v5 Reorder the terms: 28v3 + 16v4 + -12v5 = -28v3 + 28v3 + -16v4 + 16v4 + 12v5 + -12v5 Combine like terms: -28v3 + 28v3 = 0 28v3 + 16v4 + -12v5 = 0 + -16v4 + 16v4 + 12v5 + -12v5 28v3 + 16v4 + -12v5 = -16v4 + 16v4 + 12v5 + -12v5 Combine like terms: -16v4 + 16v4 = 0 28v3 + 16v4 + -12v5 = 0 + 12v5 + -12v5 28v3 + 16v4 + -12v5 = 12v5 + -12v5 Combine like terms: 12v5 + -12v5 = 0 28v3 + 16v4 + -12v5 = 0 Factor out the Greatest Common Factor (GCF), '4v3'. 4v3(7 + 4v + -3v2) = 0 Factor a trinomial. 4v3((7 + -3v)(1 + v)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'v3' equal to zero and attempt to solve: Simplifying v3 = 0 Solving v3 = 0 Move all terms containing v to the left, all other terms to the right. Simplifying v3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(7 + -3v)' equal to zero and attempt to solve: Simplifying 7 + -3v = 0 Solving 7 + -3v = 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 + -3v = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3v = 0 + -7 -3v = 0 + -7 Combine like terms: 0 + -7 = -7 -3v = -7 Divide each side by '-3'. v = 2.333333333 Simplifying v = 2.333333333Subproblem 3
Set the factor '(1 + v)' equal to zero and attempt to solve: Simplifying 1 + v = 0 Solving 1 + v = 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 + v = 0 + -1 Combine like terms: 1 + -1 = 0 0 + v = 0 + -1 v = 0 + -1 Combine like terms: 0 + -1 = -1 v = -1 Simplifying v = -1Solution
v = {2.333333333, -1}
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