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Simplifying 6u3v + -5u2v2 + -6uv3 = 0 Reorder the terms: -6uv3 + -5u2v2 + 6u3v = 0 Solving -6uv3 + -5u2v2 + 6u3v = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), 'uv'. uv(-6v2 + -5uv + 6u2) = 0 Factor a trinomial. uv((-2v + -3u)(3v + -2u)) = 0Subproblem 1
Set the factor 'uv' equal to zero and attempt to solve: Simplifying uv = 0 Solving uv = 0 Move all terms containing u to the left, all other terms to the right. Simplifying uv = 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 '(-2v + -3u)' equal to zero and attempt to solve: Simplifying -2v + -3u = 0 Reorder the terms: -3u + -2v = 0 Solving -3u + -2v = 0 Move all terms containing u to the left, all other terms to the right. Add '2v' to each side of the equation. -3u + -2v + 2v = 0 + 2v Combine like terms: -2v + 2v = 0 -3u + 0 = 0 + 2v -3u = 0 + 2v Remove the zero: -3u = 2v Divide each side by '-3'. u = -0.6666666667v Simplifying u = -0.6666666667vSubproblem 3
Set the factor '(3v + -2u)' equal to zero and attempt to solve: Simplifying 3v + -2u = 0 Reorder the terms: -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 = 1.5vSolution
u = {-0.6666666667v, 1.5v}
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