3n^2+31n+56=0

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Solution for 3n^2+31n+56=0 equation: 


Simplifying
3n2 + 31n + 56 = 0

Reorder the terms:
56 + 31n + 3n2 = 0

Solving
56 + 31n + 3n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(8 + n)(7 + 3n) = 0


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

Simplifying
8 + n = 0

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

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

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

Simplifying
n = -8

Subproblem 2
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 = -2.333333333
Solution
n = {-8, -2.333333333}

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