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Simplifying 12n2 + 28n + -5 = 0 Reorder the terms: -5 + 28n + 12n2 = 0 Solving -5 + 28n + 12n2 = 0 Solving for variable 'n'. Factor a trinomial. (-5 + -2n)(1 + -6n) = 0Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve: Simplifying -5 + -2n = 0 Solving -5 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2n = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2n = 0 + 5 -2n = 0 + 5 Combine like terms: 0 + 5 = 5 -2n = 5 Divide each side by '-2'. n = -2.5 Simplifying n = -2.5Subproblem 2
Set the factor '(1 + -6n)' equal to zero and attempt to solve: Simplifying 1 + -6n = 0 Solving 1 + -6n = 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 + -6n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6n = 0 + -1 -6n = 0 + -1 Combine like terms: 0 + -1 = -1 -6n = -1 Divide each side by '-6'. n = 0.1666666667 Simplifying n = 0.1666666667Solution
n = {-2.5, 0.1666666667}
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