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Simplifying 9n9 + -36n8 + -540n7 = 0 Reorder the terms: -540n7 + -36n8 + 9n9 = 0 Solving -540n7 + -36n8 + 9n9 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '9n7'. 9n7(-60 + -4n + n2) = 0 Factor a trinomial. 9n7((-6 + -1n)(10 + -1n)) = 0 Ignore the factor 9.Subproblem 1
Set the factor 'n7' equal to zero and attempt to solve: Simplifying n7 = 0 Solving n7 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n7 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-6 + -1n)' equal to zero and attempt to solve: Simplifying -6 + -1n = 0 Solving -6 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1n = 0 + 6 -1n = 0 + 6 Combine like terms: 0 + 6 = 6 -1n = 6 Divide each side by '-1'. n = -6 Simplifying n = -6Subproblem 3
Set the factor '(10 + -1n)' equal to zero and attempt to solve: Simplifying 10 + -1n = 0 Solving 10 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1n = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1n = 0 + -10 -1n = 0 + -10 Combine like terms: 0 + -10 = -10 -1n = -10 Divide each side by '-1'. n = 10 Simplifying n = 10Solution
n = {-6, 10}
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