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Simplifying 6 + 3[4[2(7n + -3) + -6(4n + 7) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] Reorder the terms: 6 + 3[4[2(-3 + 7n) + -6(4n + 7) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[4[(-3 * 2 + 7n * 2) + -6(4n + 7) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[4[(-6 + 14n) + -6(4n + 7) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] Reorder the terms: 6 + 3[4[-6 + 14n + -6(7 + 4n) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[4[-6 + 14n + (7 * -6 + 4n * -6) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[4[-6 + 14n + (-42 + -24n) + -3] + 9n] = 2 + -5[3(6n + -2) + 7] Reorder the terms: 6 + 3[4[-6 + -42 + -3 + 14n + -24n] + 9n] = 2 + -5[3(6n + -2) + 7] Combine like terms: -6 + -42 = -48 6 + 3[4[-48 + -3 + 14n + -24n] + 9n] = 2 + -5[3(6n + -2) + 7] Combine like terms: -48 + -3 = -51 6 + 3[4[-51 + 14n + -24n] + 9n] = 2 + -5[3(6n + -2) + 7] Combine like terms: 14n + -24n = -10n 6 + 3[4[-51 + -10n] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[[-51 * 4 + -10n * 4] + 9n] = 2 + -5[3(6n + -2) + 7] 6 + 3[[-204 + -40n] + 9n] = 2 + -5[3(6n + -2) + 7] Combine like terms: -40n + 9n = -31n 6 + 3[-204 + -31n] = 2 + -5[3(6n + -2) + 7] 6 + [-204 * 3 + -31n * 3] = 2 + -5[3(6n + -2) + 7] 6 + [-612 + -93n] = 2 + -5[3(6n + -2) + 7] Combine like terms: 6 + -612 = -606 -606 + -93n = 2 + -5[3(6n + -2) + 7] Reorder the terms: -606 + -93n = 2 + -5[3(-2 + 6n) + 7] -606 + -93n = 2 + -5[(-2 * 3 + 6n * 3) + 7] -606 + -93n = 2 + -5[(-6 + 18n) + 7] Reorder the terms: -606 + -93n = 2 + -5[-6 + 7 + 18n] Combine like terms: -6 + 7 = 1 -606 + -93n = 2 + -5[1 + 18n] -606 + -93n = 2 + [1 * -5 + 18n * -5] -606 + -93n = 2 + [-5 + -90n] Combine like terms: 2 + -5 = -3 -606 + -93n = -3 + -90n Solving -606 + -93n = -3 + -90n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '90n' to each side of the equation. -606 + -93n + 90n = -3 + -90n + 90n Combine like terms: -93n + 90n = -3n -606 + -3n = -3 + -90n + 90n Combine like terms: -90n + 90n = 0 -606 + -3n = -3 + 0 -606 + -3n = -3 Add '606' to each side of the equation. -606 + 606 + -3n = -3 + 606 Combine like terms: -606 + 606 = 0 0 + -3n = -3 + 606 -3n = -3 + 606 Combine like terms: -3 + 606 = 603 -3n = 603 Divide each side by '-3'. n = -201 Simplifying n = -201
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