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Simplifying 3mn + 2m + 12n + 8 = (m + 4)(7 + 2) Reorder the terms: 8 + 2m + 3mn + 12n = (m + 4)(7 + 2) Reorder the terms: 8 + 2m + 3mn + 12n = (4 + m)(7 + 2) Combine like terms: 7 + 2 = 9 8 + 2m + 3mn + 12n = (4 + m)(9) Reorder the terms for easier multiplication: 8 + 2m + 3mn + 12n = 9(4 + m) 8 + 2m + 3mn + 12n = (4 * 9 + m * 9) 8 + 2m + 3mn + 12n = (36 + 9m) Solving 8 + 2m + 3mn + 12n = 36 + 9m Solving for variable 'm'. Move all terms containing m to the left, all other terms to the right. Add '-9m' to each side of the equation. 8 + 2m + 3mn + -9m + 12n = 36 + 9m + -9m Reorder the terms: 8 + 2m + -9m + 3mn + 12n = 36 + 9m + -9m Combine like terms: 2m + -9m = -7m 8 + -7m + 3mn + 12n = 36 + 9m + -9m Combine like terms: 9m + -9m = 0 8 + -7m + 3mn + 12n = 36 + 0 8 + -7m + 3mn + 12n = 36 Add '-8' to each side of the equation. 8 + -7m + 3mn + -8 + 12n = 36 + -8 Reorder the terms: 8 + -8 + -7m + 3mn + 12n = 36 + -8 Combine like terms: 8 + -8 = 0 0 + -7m + 3mn + 12n = 36 + -8 -7m + 3mn + 12n = 36 + -8 Combine like terms: 36 + -8 = 28 -7m + 3mn + 12n = 28 Add '-12n' to each side of the equation. -7m + 3mn + 12n + -12n = 28 + -12n Combine like terms: 12n + -12n = 0 -7m + 3mn + 0 = 28 + -12n -7m + 3mn = 28 + -12n Reorder the terms: -28 + -7m + 3mn + 12n = 28 + -12n + -28 + 12n Reorder the terms: -28 + -7m + 3mn + 12n = 28 + -28 + -12n + 12n Combine like terms: 28 + -28 = 0 -28 + -7m + 3mn + 12n = 0 + -12n + 12n -28 + -7m + 3mn + 12n = -12n + 12n Combine like terms: -12n + 12n = 0 -28 + -7m + 3mn + 12n = 0 The solution to this equation could not be determined.
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