3n^2+45=-24n

Solution for 3n^2+45=-24n equation:

Simplifying
3n2 + 45 = -24n

Reorder the terms:
45 + 3n2 = -24n

Solving
45 + 3n2 = -24n

Solving for variable 'n'.

Reorder the terms:
45 + 24n + 3n2 = -24n + 24n

Combine like terms: -24n + 24n = 0
45 + 24n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8n + n2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {-5, -3}