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Simplifying An = n2 + 3n Reorder the terms: nA = 3n + n2 Solving nA = 3n + n2 Solving for variable 'n'. Reorder the terms: -3n + nA + -1n2 = 3n + n2 + -3n + -1n2 Reorder the terms: -3n + nA + -1n2 = 3n + -3n + n2 + -1n2 Combine like terms: 3n + -3n = 0 -3n + nA + -1n2 = 0 + n2 + -1n2 -3n + nA + -1n2 = n2 + -1n2 Combine like terms: n2 + -1n2 = 0 -3n + nA + -1n2 = 0 Factor out the Greatest Common Factor (GCF), 'n'. n(-3 + A + -1n) = 0Subproblem 1
Set the factor 'n' equal to zero and attempt to solve: Simplifying n = 0 Solving n = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n = 0Subproblem 2
Set the factor '(-3 + A + -1n)' equal to zero and attempt to solve: Simplifying -3 + A + -1n = 0 Solving -3 + A + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + A + 3 + -1n = 0 + 3 Reorder the terms: -3 + 3 + A + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + A + -1n = 0 + 3 A + -1n = 0 + 3 Combine like terms: 0 + 3 = 3 A + -1n = 3 Add '-1A' to each side of the equation. A + -1A + -1n = 3 + -1A Combine like terms: A + -1A = 0 0 + -1n = 3 + -1A -1n = 3 + -1A Divide each side by '-1'. n = -3 + A Simplifying n = -3 + ASolution
n = {0, -3 + A}
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