9n^2+36n+324=313

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Solution for 9n^2+36n+324=313 equation:


Simplifying
9n2 + 36n + 324 = 313

Reorder the terms:
324 + 36n + 9n2 = 313

Solving
324 + 36n + 9n2 = 313

Solving for variable 'n'.

Reorder the terms:
324 + -313 + 36n + 9n2 = 313 + -313

Combine like terms: 324 + -313 = 11
11 + 36n + 9n2 = 313 + -313

Combine like terms: 313 + -313 = 0
11 + 36n + 9n2 = 0

Factor a trinomial.
(11 + 3n)(1 + 3n) = 0

Subproblem 1

Set the factor '(11 + 3n)' equal to zero and attempt to solve: Simplifying 11 + 3n = 0 Solving 11 + 3n = 0 Move all terms containing n to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + 3n = 0 + -11 Combine like terms: 11 + -11 = 0 0 + 3n = 0 + -11 3n = 0 + -11 Combine like terms: 0 + -11 = -11 3n = -11 Divide each side by '3'. n = -3.666666667 Simplifying n = -3.666666667

Subproblem 2

Set the factor '(1 + 3n)' equal to zero and attempt to solve: Simplifying 1 + 3n = 0 Solving 1 + 3n = 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 + 3n = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3n = 0 + -1 3n = 0 + -1 Combine like terms: 0 + -1 = -1 3n = -1 Divide each side by '3'. n = -0.3333333333 Simplifying n = -0.3333333333

Solution

n = {-3.666666667, -0.3333333333}

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