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Simplifying 2n2 + 4n + 1 = (2n + 1)(n + 1) Reorder the terms: 1 + 4n + 2n2 = (2n + 1)(n + 1) Reorder the terms: 1 + 4n + 2n2 = (1 + 2n)(n + 1) Reorder the terms: 1 + 4n + 2n2 = (1 + 2n)(1 + n) Multiply (1 + 2n) * (1 + n) 1 + 4n + 2n2 = (1(1 + n) + 2n * (1 + n)) 1 + 4n + 2n2 = ((1 * 1 + n * 1) + 2n * (1 + n)) 1 + 4n + 2n2 = ((1 + 1n) + 2n * (1 + n)) 1 + 4n + 2n2 = (1 + 1n + (1 * 2n + n * 2n)) 1 + 4n + 2n2 = (1 + 1n + (2n + 2n2)) Combine like terms: 1n + 2n = 3n 1 + 4n + 2n2 = (1 + 3n + 2n2) Add '-1' to each side of the equation. 1 + 4n + -1 + 2n2 = 1 + 3n + -1 + 2n2 Reorder the terms: 1 + -1 + 4n + 2n2 = 1 + 3n + -1 + 2n2 Combine like terms: 1 + -1 = 0 0 + 4n + 2n2 = 1 + 3n + -1 + 2n2 4n + 2n2 = 1 + 3n + -1 + 2n2 Reorder the terms: 4n + 2n2 = 1 + -1 + 3n + 2n2 Combine like terms: 1 + -1 = 0 4n + 2n2 = 0 + 3n + 2n2 4n + 2n2 = 3n + 2n2 Add '-2n2' to each side of the equation. 4n + 2n2 + -2n2 = 3n + 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 4n + 0 = 3n + 2n2 + -2n2 4n = 3n + 2n2 + -2n2 Combine like terms: 2n2 + -2n2 = 0 4n = 3n + 0 4n = 3n Solving 4n = 3n Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3n' to each side of the equation. 4n + -3n = 3n + -3n Combine like terms: 4n + -3n = 1n 1n = 3n + -3n Combine like terms: 3n + -3n = 0 1n = 0 Divide each side by '1'. n = 0 Simplifying n = 0
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