-3n^2-5n+37=1-8n

Solution for -3n^2-5n+37=1-8n equation:

Simplifying
-3n2 + -5n + 37 = 1 + -8n

Reorder the terms:
37 + -5n + -3n2 = 1 + -8n

Solving
37 + -5n + -3n2 = 1 + -8n

Solving for variable 'n'.

Reorder the terms:
37 + -1 + -5n + 8n + -3n2 = 1 + -8n + -1 + 8n

Combine like terms: 37 + -1 = 36
36 + -5n + 8n + -3n2 = 1 + -8n + -1 + 8n

Combine like terms: -5n + 8n = 3n
36 + 3n + -3n2 = 1 + -8n + -1 + 8n

Reorder the terms:
36 + 3n + -3n2 = 1 + -1 + -8n + 8n

Combine like terms: 1 + -1 = 0
36 + 3n + -3n2 = 0 + -8n + 8n
36 + 3n + -3n2 = -8n + 8n

Combine like terms: -8n + 8n = 0
36 + 3n + -3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + n + -1n2) = 0

Factor a trinomial.
3((4 + -1n)(3 + n)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1n)' equal to zero and attempt to solve:

Simplifying
4 + -1n = 0

Solving
4 + -1n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

Simplifying
n = 4
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 = {4, -3}