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Simplifying 6n2 + 11n + -28 = 7 Reorder the terms: -28 + 11n + 6n2 = 7 Solving -28 + 11n + 6n2 = 7 Solving for variable 'n'. Reorder the terms: -28 + -7 + 11n + 6n2 = 7 + -7 Combine like terms: -28 + -7 = -35 -35 + 11n + 6n2 = 7 + -7 Combine like terms: 7 + -7 = 0 -35 + 11n + 6n2 = 0 Factor a trinomial. (-7 + -2n)(5 + -3n) = 0Subproblem 1
Set the factor '(-7 + -2n)' equal to zero and attempt to solve: Simplifying -7 + -2n = 0 Solving -7 + -2n = 0 Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -2n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2n = 0 + 7 -2n = 0 + 7 Combine like terms: 0 + 7 = 7 -2n = 7 Divide each side by '-2'. n = -3.5 Simplifying n = -3.5Subproblem 2
Set the factor '(5 + -3n)' equal to zero and attempt to solve: Simplifying 5 + -3n = 0 Solving 5 + -3n = 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 + -3n = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3n = 0 + -5 -3n = 0 + -5 Combine like terms: 0 + -5 = -5 -3n = -5 Divide each side by '-3'. n = 1.666666667 Simplifying n = 1.666666667Solution
n = {-3.5, 1.666666667}
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