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Simplifying (5m + 6n)(5m + -6n) = 0 Multiply (5m + 6n) * (5m + -6n) (5m * (5m + -6n) + 6n * (5m + -6n)) = 0 ((5m * 5m + -6n * 5m) + 6n * (5m + -6n)) = 0 Reorder the terms: ((-30mn + 25m2) + 6n * (5m + -6n)) = 0 ((-30mn + 25m2) + 6n * (5m + -6n)) = 0 (-30mn + 25m2 + (5m * 6n + -6n * 6n)) = 0 (-30mn + 25m2 + (30mn + -36n2)) = 0 Reorder the terms: (-30mn + 30mn + 25m2 + -36n2) = 0 Combine like terms: -30mn + 30mn = 0 (0 + 25m2 + -36n2) = 0 (25m2 + -36n2) = 0 Solving 25m2 + -36n2 = 0 Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '36n2' to each side of the equation. 25m2 + -36n2 + 36n2 = 0 + 36n2 Combine like terms: -36n2 + 36n2 = 0 25m2 + 0 = 0 + 36n2 25m2 = 0 + 36n2 Remove the zero: 25m2 = 36n2 Divide each side by '25'. m2 = 1.44n2 Simplifying m2 = 1.44n2 Take the square root of each side: m = {-1.2n, 1.2n}
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