3n^2+105=-36n

Solution for 3n^2+105=-36n equation:

Simplifying
3n2 + 105 = -36n

Reorder the terms:
105 + 3n2 = -36n

Solving
105 + 3n2 = -36n

Solving for variable 'n'.

Reorder the terms:
105 + 36n + 3n2 = -36n + 36n

Combine like terms: -36n + 36n = 0
105 + 36n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(35 + 12n + n2) = 0

Factor a trinomial.
3((7 + n)(5 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(7 + n)' equal to zero and attempt to solve:

Simplifying
7 + n = 0

Solving
7 + n = 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 + n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + n = 0 + -7
n = 0 + -7

Combine like terms: 0 + -7 = -7
n = -7

Simplifying
n = -7
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {-7, -5}