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Simplifying 6n2 = -5n + 21 Reorder the terms: 6n2 = 21 + -5n Solving 6n2 = 21 + -5n Solving for variable 'n'. Reorder the terms: -21 + 5n + 6n2 = 21 + -5n + -21 + 5n Reorder the terms: -21 + 5n + 6n2 = 21 + -21 + -5n + 5n Combine like terms: 21 + -21 = 0 -21 + 5n + 6n2 = 0 + -5n + 5n -21 + 5n + 6n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -21 + 5n + 6n2 = 0 Factor a trinomial. (-7 + -3n)(3 + -2n) = 0Subproblem 1
Set the factor '(-7 + -3n)' equal to zero and attempt to solve: Simplifying -7 + -3n = 0 Solving -7 + -3n = 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 + -3n = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -3n = 0 + 7 -3n = 0 + 7 Combine like terms: 0 + 7 = 7 -3n = 7 Divide each side by '-3'. n = -2.333333333 Simplifying n = -2.333333333Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve: Simplifying 3 + -2n = 0 Solving 3 + -2n = 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 + -2n = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2n = 0 + -3 -2n = 0 + -3 Combine like terms: 0 + -3 = -3 -2n = -3 Divide each side by '-2'. n = 1.5 Simplifying n = 1.5Solution
n = {-2.333333333, 1.5}
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