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Simplifying 20u2 + -54uv + 36v2 = 0 Reorder the terms: -54uv + 20u2 + 36v2 = 0 Solving -54uv + 20u2 + 36v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2'. 2(-27uv + 10u2 + 18v2) = 0 Factor a trinomial. 2((2u + -3v)(5u + -6v)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2u + -3v)' equal to zero and attempt to solve: Simplifying 2u + -3v = 0 Solving 2u + -3v = 0 Move all terms containing u to the left, all other terms to the right. Add '3v' to each side of the equation. 2u + -3v + 3v = 0 + 3v Combine like terms: -3v + 3v = 0 2u + 0 = 0 + 3v 2u = 0 + 3v Remove the zero: 2u = 3v Divide each side by '2'. u = 1.5v Simplifying u = 1.5vSubproblem 2
Set the factor '(5u + -6v)' equal to zero and attempt to solve: Simplifying 5u + -6v = 0 Solving 5u + -6v = 0 Move all terms containing u to the left, all other terms to the right. Add '6v' to each side of the equation. 5u + -6v + 6v = 0 + 6v Combine like terms: -6v + 6v = 0 5u + 0 = 0 + 6v 5u = 0 + 6v Remove the zero: 5u = 6v Divide each side by '5'. u = 1.2v Simplifying u = 1.2vSolution
u = {1.5v, 1.2v}
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