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Simplifying 35n2 = 6 + -23n Solving 35n2 = 6 + -23n Solving for variable 'n'. Reorder the terms: -6 + 23n + 35n2 = 6 + -23n + -6 + 23n Reorder the terms: -6 + 23n + 35n2 = 6 + -6 + -23n + 23n Combine like terms: 6 + -6 = 0 -6 + 23n + 35n2 = 0 + -23n + 23n -6 + 23n + 35n2 = -23n + 23n Combine like terms: -23n + 23n = 0 -6 + 23n + 35n2 = 0 Factor a trinomial. (-6 + -7n)(1 + -5n) = 0Subproblem 1
Set the factor '(-6 + -7n)' equal to zero and attempt to solve: Simplifying -6 + -7n = 0 Solving -6 + -7n = 0 Move all terms containing n to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -7n = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -7n = 0 + 6 -7n = 0 + 6 Combine like terms: 0 + 6 = 6 -7n = 6 Divide each side by '-7'. n = -0.8571428571 Simplifying n = -0.8571428571Subproblem 2
Set the factor '(1 + -5n)' equal to zero and attempt to solve: Simplifying 1 + -5n = 0 Solving 1 + -5n = 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 + -5n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5n = 0 + -1 -5n = 0 + -1 Combine like terms: 0 + -1 = -1 -5n = -1 Divide each side by '-5'. n = 0.2 Simplifying n = 0.2Solution
n = {-0.8571428571, 0.2}
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