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Simplifying 2(3n + -2) + -3(5n + 2) = 5n + -52 Reorder the terms: 2(-2 + 3n) + -3(5n + 2) = 5n + -52 (-2 * 2 + 3n * 2) + -3(5n + 2) = 5n + -52 (-4 + 6n) + -3(5n + 2) = 5n + -52 Reorder the terms: -4 + 6n + -3(2 + 5n) = 5n + -52 -4 + 6n + (2 * -3 + 5n * -3) = 5n + -52 -4 + 6n + (-6 + -15n) = 5n + -52 Reorder the terms: -4 + -6 + 6n + -15n = 5n + -52 Combine like terms: -4 + -6 = -10 -10 + 6n + -15n = 5n + -52 Combine like terms: 6n + -15n = -9n -10 + -9n = 5n + -52 Reorder the terms: -10 + -9n = -52 + 5n Solving -10 + -9n = -52 + 5n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-5n' to each side of the equation. -10 + -9n + -5n = -52 + 5n + -5n Combine like terms: -9n + -5n = -14n -10 + -14n = -52 + 5n + -5n Combine like terms: 5n + -5n = 0 -10 + -14n = -52 + 0 -10 + -14n = -52 Add '10' to each side of the equation. -10 + 10 + -14n = -52 + 10 Combine like terms: -10 + 10 = 0 0 + -14n = -52 + 10 -14n = -52 + 10 Combine like terms: -52 + 10 = -42 -14n = -42 Divide each side by '-14'. n = 3 Simplifying n = 3
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