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Simplifying 7n2 = 84n + -224 Reorder the terms: 7n2 = -224 + 84n Solving 7n2 = -224 + 84n Solving for variable 'n'. Reorder the terms: 224 + -84n + 7n2 = -224 + 84n + 224 + -84n Reorder the terms: 224 + -84n + 7n2 = -224 + 224 + 84n + -84n Combine like terms: -224 + 224 = 0 224 + -84n + 7n2 = 0 + 84n + -84n 224 + -84n + 7n2 = 84n + -84n Combine like terms: 84n + -84n = 0 224 + -84n + 7n2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(32 + -12n + n2) = 0 Factor a trinomial. 7((4 + -1n)(8 + -1n)) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve: Simplifying 4 + -1n = 0 Solving 4 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1n = 0 + -4 -1n = 0 + -4 Combine like terms: 0 + -4 = -4 -1n = -4 Divide each side by '-1'. n = 4 Simplifying n = 4Subproblem 2
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 = {4, 8}
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