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Simplifying -24u2 + -6uv + 9v2 = 0 Reorder the terms: -6uv + -24u2 + 9v2 = 0 Solving -6uv + -24u2 + 9v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2uv + -8u2 + 3v2) = 0 Factor a trinomial. 3((-4u + -3v)(2u + -1v)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4u + -3v)' equal to zero and attempt to solve: Simplifying -4u + -3v = 0 Solving -4u + -3v = 0 Move all terms containing u to the left, all other terms to the right. Add '3v' to each side of the equation. -4u + -3v + 3v = 0 + 3v Combine like terms: -3v + 3v = 0 -4u + 0 = 0 + 3v -4u = 0 + 3v Remove the zero: -4u = 3v Divide each side by '-4'. u = -0.75v Simplifying u = -0.75vSubproblem 2
Set the factor '(2u + -1v)' equal to zero and attempt to solve: Simplifying 2u + -1v = 0 Solving 2u + -1v = 0 Move all terms containing u to the left, all other terms to the right. Add 'v' to each side of the equation. 2u + -1v + v = 0 + v Combine like terms: -1v + v = 0 2u + 0 = 0 + v 2u = 0 + v Remove the zero: 2u = v Divide each side by '2'. u = 0.5v Simplifying u = 0.5vSolution
u = {-0.75v, 0.5v}
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