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Simplifying 392n2 + 231n = 7n + 40 Reorder the terms: 231n + 392n2 = 7n + 40 Reorder the terms: 231n + 392n2 = 40 + 7n Solving 231n + 392n2 = 40 + 7n Solving for variable 'n'. Reorder the terms: -40 + 231n + -7n + 392n2 = 40 + 7n + -40 + -7n Combine like terms: 231n + -7n = 224n -40 + 224n + 392n2 = 40 + 7n + -40 + -7n Reorder the terms: -40 + 224n + 392n2 = 40 + -40 + 7n + -7n Combine like terms: 40 + -40 = 0 -40 + 224n + 392n2 = 0 + 7n + -7n -40 + 224n + 392n2 = 7n + -7n Combine like terms: 7n + -7n = 0 -40 + 224n + 392n2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-5 + 28n + 49n2) = 0 Factor a trinomial. 8((-5 + -7n)(1 + -7n)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-5 + -7n)' equal to zero and attempt to solve: Simplifying -5 + -7n = 0 Solving -5 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -7n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7n = 0 + 5 -7n = 0 + 5 Combine like terms: 0 + 5 = 5 -7n = 5 Divide each side by '-7'. n = -0.7142857143 Simplifying n = -0.7142857143Subproblem 2
Set the factor '(1 + -7n)' equal to zero and attempt to solve: Simplifying 1 + -7n = 0 Solving 1 + -7n = 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 + -7n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7n = 0 + -1 -7n = 0 + -1 Combine like terms: 0 + -1 = -1 -7n = -1 Divide each side by '-7'. n = 0.1428571429 Simplifying n = 0.1428571429Solution
n = {-0.7142857143, 0.1428571429}
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