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Simplifying (2m + 3n)(2m + 3n)(2m + 3n)(2m + 3n) = 0 Multiply (2m + 3n) * (2m + 3n) (2m * (2m + 3n) + 3n * (2m + 3n))(2m + 3n)(2m + 3n) = 0 ((2m * 2m + 3n * 2m) + 3n * (2m + 3n))(2m + 3n)(2m + 3n) = 0 Reorder the terms: ((6mn + 4m2) + 3n * (2m + 3n))(2m + 3n)(2m + 3n) = 0 ((6mn + 4m2) + 3n * (2m + 3n))(2m + 3n)(2m + 3n) = 0 (6mn + 4m2 + (2m * 3n + 3n * 3n))(2m + 3n)(2m + 3n) = 0 (6mn + 4m2 + (6mn + 9n2))(2m + 3n)(2m + 3n) = 0 Reorder the terms: (6mn + 6mn + 4m2 + 9n2)(2m + 3n)(2m + 3n) = 0 Combine like terms: 6mn + 6mn = 12mn (12mn + 4m2 + 9n2)(2m + 3n)(2m + 3n) = 0 Multiply (12mn + 4m2 + 9n2) * (2m + 3n) (12mn * (2m + 3n) + 4m2 * (2m + 3n) + 9n2 * (2m + 3n))(2m + 3n) = 0 ((2m * 12mn + 3n * 12mn) + 4m2 * (2m + 3n) + 9n2 * (2m + 3n))(2m + 3n) = 0 Reorder the terms: ((36mn2 + 24m2n) + 4m2 * (2m + 3n) + 9n2 * (2m + 3n))(2m + 3n) = 0 ((36mn2 + 24m2n) + 4m2 * (2m + 3n) + 9n2 * (2m + 3n))(2m + 3n) = 0 (36mn2 + 24m2n + (2m * 4m2 + 3n * 4m2) + 9n2 * (2m + 3n))(2m + 3n) = 0 Reorder the terms: (36mn2 + 24m2n + (12m2n + 8m3) + 9n2 * (2m + 3n))(2m + 3n) = 0 (36mn2 + 24m2n + (12m2n + 8m3) + 9n2 * (2m + 3n))(2m + 3n) = 0 (36mn2 + 24m2n + 12m2n + 8m3 + (2m * 9n2 + 3n * 9n2))(2m + 3n) = 0 (36mn2 + 24m2n + 12m2n + 8m3 + (18mn2 + 27n3))(2m + 3n) = 0 Reorder the terms: (36mn2 + 18mn2 + 24m2n + 12m2n + 8m3 + 27n3)(2m + 3n) = 0 Combine like terms: 36mn2 + 18mn2 = 54mn2 (54mn2 + 24m2n + 12m2n + 8m3 + 27n3)(2m + 3n) = 0 Combine like terms: 24m2n + 12m2n = 36m2n (54mn2 + 36m2n + 8m3 + 27n3)(2m + 3n) = 0 Multiply (54mn2 + 36m2n + 8m3 + 27n3) * (2m + 3n) (54mn2 * (2m + 3n) + 36m2n * (2m + 3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 ((2m * 54mn2 + 3n * 54mn2) + 36m2n * (2m + 3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 Reorder the terms: ((162mn3 + 108m2n2) + 36m2n * (2m + 3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 ((162mn3 + 108m2n2) + 36m2n * (2m + 3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 (162mn3 + 108m2n2 + (2m * 36m2n + 3n * 36m2n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 Reorder the terms: (162mn3 + 108m2n2 + (108m2n2 + 72m3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 (162mn3 + 108m2n2 + (108m2n2 + 72m3n) + 8m3 * (2m + 3n) + 27n3 * (2m + 3n)) = 0 (162mn3 + 108m2n2 + 108m2n2 + 72m3n + (2m * 8m3 + 3n * 8m3) + 27n3 * (2m + 3n)) = 0 Reorder the terms: (162mn3 + 108m2n2 + 108m2n2 + 72m3n + (24m3n + 16m4) + 27n3 * (2m + 3n)) = 0 (162mn3 + 108m2n2 + 108m2n2 + 72m3n + (24m3n + 16m4) + 27n3 * (2m + 3n)) = 0 (162mn3 + 108m2n2 + 108m2n2 + 72m3n + 24m3n + 16m4 + (2m * 27n3 + 3n * 27n3)) = 0 (162mn3 + 108m2n2 + 108m2n2 + 72m3n + 24m3n + 16m4 + (54mn3 + 81n4)) = 0 Reorder the terms: (162mn3 + 54mn3 + 108m2n2 + 108m2n2 + 72m3n + 24m3n + 16m4 + 81n4) = 0 Combine like terms: 162mn3 + 54mn3 = 216mn3 (216mn3 + 108m2n2 + 108m2n2 + 72m3n + 24m3n + 16m4 + 81n4) = 0 Combine like terms: 108m2n2 + 108m2n2 = 216m2n2 (216mn3 + 216m2n2 + 72m3n + 24m3n + 16m4 + 81n4) = 0 Combine like terms: 72m3n + 24m3n = 96m3n (216mn3 + 216m2n2 + 96m3n + 16m4 + 81n4) = 0 Solving 216mn3 + 216m2n2 + 96m3n + 16m4 + 81n4 = 0 Solving for variable 'm'. The solution to this equation could not be determined.
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