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Simplifying 7n5 + -56n3 = 49n4 Reorder the terms: -56n3 + 7n5 = 49n4 Solving -56n3 + 7n5 = 49n4 Solving for variable 'n'. Reorder the terms: -56n3 + -49n4 + 7n5 = 49n4 + -49n4 Combine like terms: 49n4 + -49n4 = 0 -56n3 + -49n4 + 7n5 = 0 Factor out the Greatest Common Factor (GCF), '7n3'. 7n3(-8 + -7n + n2) = 0 Factor a trinomial. 7n3((-1 + -1n)(8 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor 'n3' equal to zero and attempt to solve: Simplifying n3 = 0 Solving n3 = 0 Move all terms containing n to the left, all other terms to the right. Simplifying n3 = 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 '(-1 + -1n)' equal to zero and attempt to solve: Simplifying -1 + -1n = 0 Solving -1 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1n = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1n = 0 + 1 -1n = 0 + 1 Combine like terms: 0 + 1 = 1 -1n = 1 Divide each side by '-1'. n = -1 Simplifying n = -1Subproblem 3
Set the factor '(8 + -1n)' equal to zero and attempt to solve: Simplifying 8 + -1n = 0 Solving 8 + -1n = 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 + -1n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1n = 0 + -8 -1n = 0 + -8 Combine like terms: 0 + -8 = -8 -1n = -8 Divide each side by '-1'. n = 8 Simplifying n = 8Solution
n = {-1, 8}
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