3n^2-53n+232=0

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Solution for 3n^2-53n+232=0 equation: 


Simplifying
3n2 + -53n + 232 = 0

Reorder the terms:
232 + -53n + 3n2 = 0

Solving
232 + -53n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + -1n)(29 + -3n) = 0


Subproblem 1
Set the factor '(8 + -1n)' equal to zero and attempt to solve:

Simplifying
8 + -1n = 0

Solving
8 + -1n = 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 + -1n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1n = 0 + -8
-1n = 0 + -8

Combine like terms: 0 + -8 = -8
-1n = -8

Divide each side by '-1'.
n = 8

Simplifying
n = 8

Subproblem 2
Set the factor '(29 + -3n)' equal to zero and attempt to solve:

Simplifying
29 + -3n = 0

Solving
29 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-29' to each side of the equation.
29 + -29 + -3n = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -3n = 0 + -29
-3n = 0 + -29

Combine like terms: 0 + -29 = -29
-3n = -29

Divide each side by '-3'.
n = 9.666666667

Simplifying
n = 9.666666667
Solution
n = {8, 9.666666667}

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