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Simplifying 21n2 = 53n + 8 Reorder the terms: 21n2 = 8 + 53n Solving 21n2 = 8 + 53n Solving for variable 'n'. Reorder the terms: -8 + -53n + 21n2 = 8 + 53n + -8 + -53n Reorder the terms: -8 + -53n + 21n2 = 8 + -8 + 53n + -53n Combine like terms: 8 + -8 = 0 -8 + -53n + 21n2 = 0 + 53n + -53n -8 + -53n + 21n2 = 53n + -53n Combine like terms: 53n + -53n = 0 -8 + -53n + 21n2 = 0 Factor a trinomial. (-1 + -7n)(8 + -3n) = 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 '(8 + -3n)' equal to zero and attempt to solve: Simplifying 8 + -3n = 0 Solving 8 + -3n = 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 + -3n = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -3n = 0 + -8 -3n = 0 + -8 Combine like terms: 0 + -8 = -8 -3n = -8 Divide each side by '-3'. n = 2.666666667 Simplifying n = 2.666666667Solution
n = {-0.1428571429, 2.666666667}
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