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Simplifying (6u + 6v)(6u + 6v) = 0 Multiply (6u + 6v) * (6u + 6v) (6u * (6u + 6v) + 6v * (6u + 6v)) = 0 ((6u * 6u + 6v * 6u) + 6v * (6u + 6v)) = 0 Reorder the terms: ((36uv + 36u2) + 6v * (6u + 6v)) = 0 ((36uv + 36u2) + 6v * (6u + 6v)) = 0 (36uv + 36u2 + (6u * 6v + 6v * 6v)) = 0 (36uv + 36u2 + (36uv + 36v2)) = 0 Reorder the terms: (36uv + 36uv + 36u2 + 36v2) = 0 Combine like terms: 36uv + 36uv = 72uv (72uv + 36u2 + 36v2) = 0 Solving 72uv + 36u2 + 36v2 = 0 Solving for variable 'u'. Factor out the Greatest Common Factor (GCF), '36'. 36(2uv + u2 + v2) = 0 Factor a trinomial. 36((u + v)(u + v)) = 0 Ignore the factor 36.Subproblem 1
Set the factor '(u + v)' equal to zero and attempt to solve: Simplifying u + v = 0 Solving u + v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. u + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 u + 0 = 0 + -1v u = 0 + -1v Remove the zero: u = -1v Simplifying u = -1vSubproblem 2
Set the factor '(u + v)' equal to zero and attempt to solve: Simplifying u + v = 0 Solving u + v = 0 Move all terms containing u to the left, all other terms to the right. Add '-1v' to each side of the equation. u + v + -1v = 0 + -1v Combine like terms: v + -1v = 0 u + 0 = 0 + -1v u = 0 + -1v Remove the zero: u = -1v Simplifying u = -1vSolution
u = {-1v, -1v}
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