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Simplifying 36x2n + 316xn + 224n = 0 Reorder the terms: 224n + 316nx + 36nx2 = 0 Solving 224n + 316nx + 36nx2 = 0 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), '4n'. 4n(56 + 79x + 9x2) = 0 Factor a trinomial. 4n((8 + x)(7 + 9x)) = 0 Ignore the factor 4.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 '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing n to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Add '-1x' to each side of the equation. x + -1x = -8 + -1x Combine like terms: x + -1x = 0 0 = -8 + -1x Simplifying 0 = -8 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(7 + 9x)' equal to zero and attempt to solve: Simplifying 7 + 9x = 0 Solving 7 + 9x = 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 + 9x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 9x = 0 + -7 9x = 0 + -7 Combine like terms: 0 + -7 = -7 9x = -7 Add '-9x' to each side of the equation. 9x + -9x = -7 + -9x Combine like terms: 9x + -9x = 0 0 = -7 + -9x Simplifying 0 = -7 + -9x 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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