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Simplifying 6u2 + 54uv + 120v2 = 0 Reorder the terms: 54uv + 6u2 + 120v2 = 0 Solving 54uv + 6u2 + 120v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '6'. 6(9uv + u2 + 20v2) = 0 Factor a trinomial. 6((u + 4v)(u + 5v)) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(u + 4v)' equal to zero and attempt to solve: Simplifying u + 4v = 0 Solving u + 4v = 0 Move all terms containing u to the left, all other terms to the right. Add '-4v' to each side of the equation. u + 4v + -4v = 0 + -4v Combine like terms: 4v + -4v = 0 u + 0 = 0 + -4v u = 0 + -4v Remove the zero: u = -4v Simplifying u = -4vSubproblem 2
Set the factor '(u + 5v)' equal to zero and attempt to solve: Simplifying u + 5v = 0 Solving u + 5v = 0 Move all terms containing u to the left, all other terms to the right. Add '-5v' to each side of the equation. u + 5v + -5v = 0 + -5v Combine like terms: 5v + -5v = 0 u + 0 = 0 + -5v u = 0 + -5v Remove the zero: u = -5v Simplifying u = -5vSolution
u = {-4v, -5v}
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