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Simplifying n(n + -7) = n2 + 3(-2n + 1) + -1 Reorder the terms: n(-7 + n) = n2 + 3(-2n + 1) + -1 (-7 * n + n * n) = n2 + 3(-2n + 1) + -1 (-7n + n2) = n2 + 3(-2n + 1) + -1 Reorder the terms: -7n + n2 = n2 + 3(1 + -2n) + -1 -7n + n2 = n2 + (1 * 3 + -2n * 3) + -1 -7n + n2 = n2 + (3 + -6n) + -1 Reorder the terms: -7n + n2 = 3 + -1 + -6n + n2 Combine like terms: 3 + -1 = 2 -7n + n2 = 2 + -6n + n2 Add '-1n2' to each side of the equation. -7n + n2 + -1n2 = 2 + -6n + n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -7n + 0 = 2 + -6n + n2 + -1n2 -7n = 2 + -6n + n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -7n = 2 + -6n + 0 -7n = 2 + -6n Solving -7n = 2 + -6n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '6n' to each side of the equation. -7n + 6n = 2 + -6n + 6n Combine like terms: -7n + 6n = -1n -1n = 2 + -6n + 6n Combine like terms: -6n + 6n = 0 -1n = 2 + 0 -1n = 2 Divide each side by '-1'. n = -2 Simplifying n = -2
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