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Simplifying 6(3n + -9) + 45 = 12 + -4(9 + -2n) Reorder the terms: 6(-9 + 3n) + 45 = 12 + -4(9 + -2n) (-9 * 6 + 3n * 6) + 45 = 12 + -4(9 + -2n) (-54 + 18n) + 45 = 12 + -4(9 + -2n) Reorder the terms: -54 + 45 + 18n = 12 + -4(9 + -2n) Combine like terms: -54 + 45 = -9 -9 + 18n = 12 + -4(9 + -2n) -9 + 18n = 12 + (9 * -4 + -2n * -4) -9 + 18n = 12 + (-36 + 8n) Combine like terms: 12 + -36 = -24 -9 + 18n = -24 + 8n Solving -9 + 18n = -24 + 8n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-8n' to each side of the equation. -9 + 18n + -8n = -24 + 8n + -8n Combine like terms: 18n + -8n = 10n -9 + 10n = -24 + 8n + -8n Combine like terms: 8n + -8n = 0 -9 + 10n = -24 + 0 -9 + 10n = -24 Add '9' to each side of the equation. -9 + 9 + 10n = -24 + 9 Combine like terms: -9 + 9 = 0 0 + 10n = -24 + 9 10n = -24 + 9 Combine like terms: -24 + 9 = -15 10n = -15 Divide each side by '10'. n = -1.5 Simplifying n = -1.5
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