17n^2+102n+63=3-n^2

Solution for 17n^2+102n+63=3-n^2 equation:

Simplifying
17n2 + 102n + 63 = 3 + -1n2

Reorder the terms:
63 + 102n + 17n2 = 3 + -1n2

Solving
63 + 102n + 17n2 = 3 + -1n2

Solving for variable 'n'.

Reorder the terms:
63 + -3 + 102n + 17n2 + n2 = 3 + -1n2 + -3 + n2

Combine like terms: 63 + -3 = 60
60 + 102n + 17n2 + n2 = 3 + -1n2 + -3 + n2

Combine like terms: 17n2 + n2 = 18n2
60 + 102n + 18n2 = 3 + -1n2 + -3 + n2

Reorder the terms:
60 + 102n + 18n2 = 3 + -3 + -1n2 + n2

Combine like terms: 3 + -3 = 0
60 + 102n + 18n2 = 0 + -1n2 + n2
60 + 102n + 18n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
60 + 102n + 18n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(10 + 17n + 3n2) = 0

Factor a trinomial.
6((5 + n)(2 + 3n)) = 0

Ignore the factor 6.
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 '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
Solution
n = {-5, -0.6666666667}