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Simplifying 2[n + -4(4n + 22) + 10] = 2(n + 12) Reorder the terms: 2[n + -4(22 + 4n) + 10] = 2(n + 12) 2[n + (22 * -4 + 4n * -4) + 10] = 2(n + 12) 2[n + (-88 + -16n) + 10] = 2(n + 12) Reorder the terms: 2[-88 + 10 + n + -16n] = 2(n + 12) Combine like terms: -88 + 10 = -78 2[-78 + n + -16n] = 2(n + 12) Combine like terms: n + -16n = -15n 2[-78 + -15n] = 2(n + 12) [-78 * 2 + -15n * 2] = 2(n + 12) [-156 + -30n] = 2(n + 12) Reorder the terms: -156 + -30n = 2(12 + n) -156 + -30n = (12 * 2 + n * 2) -156 + -30n = (24 + 2n) Solving -156 + -30n = 24 + 2n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2n' to each side of the equation. -156 + -30n + -2n = 24 + 2n + -2n Combine like terms: -30n + -2n = -32n -156 + -32n = 24 + 2n + -2n Combine like terms: 2n + -2n = 0 -156 + -32n = 24 + 0 -156 + -32n = 24 Add '156' to each side of the equation. -156 + 156 + -32n = 24 + 156 Combine like terms: -156 + 156 = 0 0 + -32n = 24 + 156 -32n = 24 + 156 Combine like terms: 24 + 156 = 180 -32n = 180 Divide each side by '-32'. n = -5.625 Simplifying n = -5.625
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