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Simplifying 7n2 = 16 + 6n Solving 7n2 = 16 + 6n Solving for variable 'n'. Reorder the terms: -16 + -6n + 7n2 = 16 + 6n + -16 + -6n Reorder the terms: -16 + -6n + 7n2 = 16 + -16 + 6n + -6n Combine like terms: 16 + -16 = 0 -16 + -6n + 7n2 = 0 + 6n + -6n -16 + -6n + 7n2 = 6n + -6n Combine like terms: 6n + -6n = 0 -16 + -6n + 7n2 = 0 Factor a trinomial. (-8 + -7n)(2 + -1n) = 0Subproblem 1
Set the factor '(-8 + -7n)' equal to zero and attempt to solve: Simplifying -8 + -7n = 0 Solving -8 + -7n = 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 + -7n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7n = 0 + 8 -7n = 0 + 8 Combine like terms: 0 + 8 = 8 -7n = 8 Divide each side by '-7'. n = -1.142857143 Simplifying n = -1.142857143Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {-1.142857143, 2}
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