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Simplifying (6u + -7v)(6u + 7v) = 0 Multiply (6u + -7v) * (6u + 7v) (6u * (6u + 7v) + -7v * (6u + 7v)) = 0 ((6u * 6u + 7v * 6u) + -7v * (6u + 7v)) = 0 Reorder the terms: ((42uv + 36u2) + -7v * (6u + 7v)) = 0 ((42uv + 36u2) + -7v * (6u + 7v)) = 0 (42uv + 36u2 + (6u * -7v + 7v * -7v)) = 0 (42uv + 36u2 + (-42uv + -49v2)) = 0 Reorder the terms: (42uv + -42uv + 36u2 + -49v2) = 0 Combine like terms: 42uv + -42uv = 0 (0 + 36u2 + -49v2) = 0 (36u2 + -49v2) = 0 Solving 36u2 + -49v2 = 0 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '49v2' to each side of the equation. 36u2 + -49v2 + 49v2 = 0 + 49v2 Combine like terms: -49v2 + 49v2 = 0 36u2 + 0 = 0 + 49v2 36u2 = 0 + 49v2 Remove the zero: 36u2 = 49v2 Divide each side by '36'. u2 = 1.361111111v2 Simplifying u2 = 1.361111111v2 Take the square root of each side: u = {-1.166666667v, 1.166666667v}
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