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Simplifying (-7n2 + 8n + -4) + -1(-11n + 2 + -14n2) = 0 Reorder the terms: (-4 + 8n + -7n2) + -1(-11n + 2 + -14n2) = 0 Remove parenthesis around (-4 + 8n + -7n2) -4 + 8n + -7n2 + -1(-11n + 2 + -14n2) = 0 Reorder the terms: -4 + 8n + -7n2 + -1(2 + -11n + -14n2) = 0 -4 + 8n + -7n2 + (2 * -1 + -11n * -1 + -14n2 * -1) = 0 -4 + 8n + -7n2 + (-2 + 11n + 14n2) = 0 Reorder the terms: -4 + -2 + 8n + 11n + -7n2 + 14n2 = 0 Combine like terms: -4 + -2 = -6 -6 + 8n + 11n + -7n2 + 14n2 = 0 Combine like terms: 8n + 11n = 19n -6 + 19n + -7n2 + 14n2 = 0 Combine like terms: -7n2 + 14n2 = 7n2 -6 + 19n + 7n2 = 0 Solving -6 + 19n + 7n2 = 0 Solving for variable 'n'. Factor a trinomial. (-3 + -1n)(2 + -7n) = 0Subproblem 1
Set the factor '(-3 + -1n)' equal to zero and attempt to solve: Simplifying -3 + -1n = 0 Solving -3 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1n = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1n = 0 + 3 -1n = 0 + 3 Combine like terms: 0 + 3 = 3 -1n = 3 Divide each side by '-1'. n = -3 Simplifying n = -3Subproblem 2
Set the factor '(2 + -7n)' equal to zero and attempt to solve: Simplifying 2 + -7n = 0 Solving 2 + -7n = 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 + -7n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -7n = 0 + -2 -7n = 0 + -2 Combine like terms: 0 + -2 = -2 -7n = -2 Divide each side by '-7'. n = 0.2857142857 Simplifying n = 0.2857142857Solution
n = {-3, 0.2857142857}
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