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Simplifying 8u3 + -24u2v + 18uv2 = 0 Reorder the terms: 18uv2 + -24u2v + 8u3 = 0 Solving 18uv2 + -24u2v + 8u3 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '2u'. 2u(9v2 + -12uv + 4u2) = 0 Factor a trinomial. 2u((3v + -2u)(3v + -2u)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'u' equal to zero and attempt to solve: Simplifying u = 0 Solving u = 0 Move all terms containing u to the left, all other terms to the right. Simplifying u = 0Subproblem 2
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 = 1.5vSubproblem 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, 1.5v, 1.5v}
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