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Simplifying (3u + 4v)(3u + 4v) = 0 Multiply (3u + 4v) * (3u + 4v) (3u * (3u + 4v) + 4v * (3u + 4v)) = 0 ((3u * 3u + 4v * 3u) + 4v * (3u + 4v)) = 0 Reorder the terms: ((12uv + 9u2) + 4v * (3u + 4v)) = 0 ((12uv + 9u2) + 4v * (3u + 4v)) = 0 (12uv + 9u2 + (3u * 4v + 4v * 4v)) = 0 (12uv + 9u2 + (12uv + 16v2)) = 0 Reorder the terms: (12uv + 12uv + 9u2 + 16v2) = 0 Combine like terms: 12uv + 12uv = 24uv (24uv + 9u2 + 16v2) = 0 Solving 24uv + 9u2 + 16v2 = 0 Solving for variable 'u'. Factor a trinomial. (3u + 4v)(3u + 4v) = 0Subproblem 1
Set the factor '(3u + 4v)' equal to zero and attempt to solve: Simplifying 3u + 4v = 0 Solving 3u + 4v = 0 Move all terms containing u to the left, all other terms to the right. Add '-4v' to each side of the equation. 3u + 4v + -4v = 0 + -4v Combine like terms: 4v + -4v = 0 3u + 0 = 0 + -4v 3u = 0 + -4v Remove the zero: 3u = -4v Divide each side by '3'. u = -1.333333333v Simplifying u = -1.333333333vSubproblem 2
Set the factor '(3u + 4v)' equal to zero and attempt to solve: Simplifying 3u + 4v = 0 Solving 3u + 4v = 0 Move all terms containing u to the left, all other terms to the right. Add '-4v' to each side of the equation. 3u + 4v + -4v = 0 + -4v Combine like terms: 4v + -4v = 0 3u + 0 = 0 + -4v 3u = 0 + -4v Remove the zero: 3u = -4v Divide each side by '3'. u = -1.333333333v Simplifying u = -1.333333333vSolution
u = {-1.333333333v, -1.333333333v}
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