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Simplifying 8(n + -15) + -6(n + 12) = 4(n + 10) Reorder the terms: 8(-15 + n) + -6(n + 12) = 4(n + 10) (-15 * 8 + n * 8) + -6(n + 12) = 4(n + 10) (-120 + 8n) + -6(n + 12) = 4(n + 10) Reorder the terms: -120 + 8n + -6(12 + n) = 4(n + 10) -120 + 8n + (12 * -6 + n * -6) = 4(n + 10) -120 + 8n + (-72 + -6n) = 4(n + 10) Reorder the terms: -120 + -72 + 8n + -6n = 4(n + 10) Combine like terms: -120 + -72 = -192 -192 + 8n + -6n = 4(n + 10) Combine like terms: 8n + -6n = 2n -192 + 2n = 4(n + 10) Reorder the terms: -192 + 2n = 4(10 + n) -192 + 2n = (10 * 4 + n * 4) -192 + 2n = (40 + 4n) Solving -192 + 2n = 40 + 4n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-4n' to each side of the equation. -192 + 2n + -4n = 40 + 4n + -4n Combine like terms: 2n + -4n = -2n -192 + -2n = 40 + 4n + -4n Combine like terms: 4n + -4n = 0 -192 + -2n = 40 + 0 -192 + -2n = 40 Add '192' to each side of the equation. -192 + 192 + -2n = 40 + 192 Combine like terms: -192 + 192 = 0 0 + -2n = 40 + 192 -2n = 40 + 192 Combine like terms: 40 + 192 = 232 -2n = 232 Divide each side by '-2'. n = -116 Simplifying n = -116
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