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Simplifying 12n + 7(n + -6) = -12(1 + -2n) Reorder the terms: 12n + 7(-6 + n) = -12(1 + -2n) 12n + (-6 * 7 + n * 7) = -12(1 + -2n) 12n + (-42 + 7n) = -12(1 + -2n) Reorder the terms: -42 + 12n + 7n = -12(1 + -2n) Combine like terms: 12n + 7n = 19n -42 + 19n = -12(1 + -2n) -42 + 19n = (1 * -12 + -2n * -12) -42 + 19n = (-12 + 24n) Solving -42 + 19n = -12 + 24n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-24n' to each side of the equation. -42 + 19n + -24n = -12 + 24n + -24n Combine like terms: 19n + -24n = -5n -42 + -5n = -12 + 24n + -24n Combine like terms: 24n + -24n = 0 -42 + -5n = -12 + 0 -42 + -5n = -12 Add '42' to each side of the equation. -42 + 42 + -5n = -12 + 42 Combine like terms: -42 + 42 = 0 0 + -5n = -12 + 42 -5n = -12 + 42 Combine like terms: -12 + 42 = 30 -5n = 30 Divide each side by '-5'. n = -6 Simplifying n = -6
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