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Simplifying 27u2 + 54uv + -21v2 = 0 Reorder the terms: 54uv + 27u2 + -21v2 = 0 Solving 54uv + 27u2 + -21v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(18uv + 9u2 + -7v2) = 0 Factor a trinomial. 3((3u + -1v)(3u + 7v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3u + -1v)' equal to zero and attempt to solve: Simplifying 3u + -1v = 0 Solving 3u + -1v = 0 Move all terms containing u to the left, all other terms to the right. Add 'v' to each side of the equation. 3u + -1v + v = 0 + v Combine like terms: -1v + v = 0 3u + 0 = 0 + v 3u = 0 + v Remove the zero: 3u = v Divide each side by '3'. u = 0.3333333333v Simplifying u = 0.3333333333vSubproblem 2
Set the factor '(3u + 7v)' equal to zero and attempt to solve: Simplifying 3u + 7v = 0 Solving 3u + 7v = 0 Move all terms containing u to the left, all other terms to the right. Add '-7v' to each side of the equation. 3u + 7v + -7v = 0 + -7v Combine like terms: 7v + -7v = 0 3u + 0 = 0 + -7v 3u = 0 + -7v Remove the zero: 3u = -7v Divide each side by '3'. u = -2.333333333v Simplifying u = -2.333333333vSolution
u = {0.3333333333v, -2.333333333v}
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