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Simplifying 3n2 + -12n + 1 = -5n + 7 Reorder the terms: 1 + -12n + 3n2 = -5n + 7 Reorder the terms: 1 + -12n + 3n2 = 7 + -5n Solving 1 + -12n + 3n2 = 7 + -5n Solving for variable 'n'. Reorder the terms: 1 + -7 + -12n + 5n + 3n2 = 7 + -5n + -7 + 5n Combine like terms: 1 + -7 = -6 -6 + -12n + 5n + 3n2 = 7 + -5n + -7 + 5n Combine like terms: -12n + 5n = -7n -6 + -7n + 3n2 = 7 + -5n + -7 + 5n Reorder the terms: -6 + -7n + 3n2 = 7 + -7 + -5n + 5n Combine like terms: 7 + -7 = 0 -6 + -7n + 3n2 = 0 + -5n + 5n -6 + -7n + 3n2 = -5n + 5n Combine like terms: -5n + 5n = 0 -6 + -7n + 3n2 = 0 Factor a trinomial. (-2 + -3n)(3 + -1n) = 0Subproblem 1
Set the factor '(-2 + -3n)' equal to zero and attempt to solve: Simplifying -2 + -3n = 0 Solving -2 + -3n = 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 + -3n = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3n = 0 + 2 -3n = 0 + 2 Combine like terms: 0 + 2 = 2 -3n = 2 Divide each side by '-3'. n = -0.6666666667 Simplifying n = -0.6666666667Subproblem 2
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 = 3Solution
n = {-0.6666666667, 3}
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