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Simplifying 9n2 + 12n + 4 = 36 Reorder the terms: 4 + 12n + 9n2 = 36 Solving 4 + 12n + 9n2 = 36 Solving for variable 'n'. Reorder the terms: 4 + -36 + 12n + 9n2 = 36 + -36 Combine like terms: 4 + -36 = -32 -32 + 12n + 9n2 = 36 + -36 Combine like terms: 36 + -36 = 0 -32 + 12n + 9n2 = 0 Factor a trinomial. (-8 + -3n)(4 + -3n) = 0Subproblem 1
Set the factor '(-8 + -3n)' equal to zero and attempt to solve: Simplifying -8 + -3n = 0 Solving -8 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -3n = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3n = 0 + 8 -3n = 0 + 8 Combine like terms: 0 + 8 = 8 -3n = 8 Divide each side by '-3'. n = -2.666666667 Simplifying n = -2.666666667Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve: Simplifying 4 + -3n = 0 Solving 4 + -3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3n = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3n = 0 + -4 -3n = 0 + -4 Combine like terms: 0 + -4 = -4 -3n = -4 Divide each side by '-3'. n = 1.333333333 Simplifying n = 1.333333333Solution
n = {-2.666666667, 1.333333333}
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