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Simplifying 1n(5x + 21) = 1n(12x + -28) Reorder the terms: 1n(21 + 5x) = 1n(12x + -28) (21 * 1n + 5x * 1n) = 1n(12x + -28) (21n + 5nx) = 1n(12x + -28) Reorder the terms: 21n + 5nx = 1n(-28 + 12x) 21n + 5nx = (-28 * 1n + 12x * 1n) 21n + 5nx = (-28n + 12nx) Solving 21n + 5nx = -28n + 12nx Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '28n' to each side of the equation. 21n + 28n + 5nx = -28n + 28n + 12nx Combine like terms: 21n + 28n = 49n 49n + 5nx = -28n + 28n + 12nx Combine like terms: -28n + 28n = 0 49n + 5nx = 0 + 12nx 49n + 5nx = 12nx Add '-12nx' to each side of the equation. 49n + 5nx + -12nx = 12nx + -12nx Combine like terms: 5nx + -12nx = -7nx 49n + -7nx = 12nx + -12nx Combine like terms: 12nx + -12nx = 0 49n + -7nx = 0 Factor out the Greatest Common Factor (GCF), '7n'. 7n(7 + -1x) = 0 Ignore the factor 7.Subproblem 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 '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing n to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Add 'x' to each side of the equation. -1x + x = -7 + x Combine like terms: -1x + x = 0 0 = -7 + x Simplifying 0 = -7 + x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
n = {0}
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