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Simplifying 7n2 = 27n + 4 Reorder the terms: 7n2 = 4 + 27n Solving 7n2 = 4 + 27n Solving for variable 'n'. Reorder the terms: -4 + -27n + 7n2 = 4 + 27n + -4 + -27n Reorder the terms: -4 + -27n + 7n2 = 4 + -4 + 27n + -27n Combine like terms: 4 + -4 = 0 -4 + -27n + 7n2 = 0 + 27n + -27n -4 + -27n + 7n2 = 27n + -27n Combine like terms: 27n + -27n = 0 -4 + -27n + 7n2 = 0 Factor a trinomial. (-1 + -7n)(4 + -1n) = 0Subproblem 1
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 = -0.1428571429Subproblem 2
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 = 4Solution
n = {-0.1428571429, 4}
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