4n^2+17n+15=-3+2n+n^2

Solution for 4n^2+17n+15=-3+2n+n^2 equation:

Simplifying
4n2 + 17n + 15 = -3 + 2n + n2

Reorder the terms:
15 + 17n + 4n2 = -3 + 2n + n2

Solving
15 + 17n + 4n2 = -3 + 2n + n2

Solving for variable 'n'.

Reorder the terms:
15 + 3 + 17n + -2n + 4n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: 15 + 3 = 18
18 + 17n + -2n + 4n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: 17n + -2n = 15n
18 + 15n + 4n2 + -1n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Combine like terms: 4n2 + -1n2 = 3n2
18 + 15n + 3n2 = -3 + 2n + n2 + 3 + -2n + -1n2

Reorder the terms:
18 + 15n + 3n2 = -3 + 3 + 2n + -2n + n2 + -1n2

Combine like terms: -3 + 3 = 0
18 + 15n + 3n2 = 0 + 2n + -2n + n2 + -1n2
18 + 15n + 3n2 = 2n + -2n + n2 + -1n2

Combine like terms: 2n + -2n = 0
18 + 15n + 3n2 = 0 + n2 + -1n2
18 + 15n + 3n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
18 + 15n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + 5n + n2) = 0

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

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

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-3, -2}