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Simplifying 3(n + -10) + -5(n + 12) = 0 Reorder the terms: 3(-10 + n) + -5(n + 12) = 0 (-10 * 3 + n * 3) + -5(n + 12) = 0 (-30 + 3n) + -5(n + 12) = 0 Reorder the terms: -30 + 3n + -5(12 + n) = 0 -30 + 3n + (12 * -5 + n * -5) = 0 -30 + 3n + (-60 + -5n) = 0 Reorder the terms: -30 + -60 + 3n + -5n = 0 Combine like terms: -30 + -60 = -90 -90 + 3n + -5n = 0 Combine like terms: 3n + -5n = -2n -90 + -2n = 0 Solving -90 + -2n = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '90' to each side of the equation. -90 + 90 + -2n = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -2n = 0 + 90 -2n = 0 + 90 Combine like terms: 0 + 90 = 90 -2n = 90 Divide each side by '-2'. n = -45 Simplifying n = -45
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