3n^2+6n-15=6

Solution for 3n^2+6n-15=6 equation:

Simplifying
3n2 + 6n + -15 = 6

Reorder the terms:
-15 + 6n + 3n2 = 6

Solving
-15 + 6n + 3n2 = 6

Solving for variable 'n'.

Reorder the terms:
-15 + -6 + 6n + 3n2 = 6 + -6

Combine like terms: -15 + -6 = -21
-21 + 6n + 3n2 = 6 + -6

Combine like terms: 6 + -6 = 0
-21 + 6n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + 2n + n2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-7 + 2n + n2)' equal to zero and attempt to solve:

Simplifying
-7 + 2n + n2 = 0

Solving
-7 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2n + 7 + n2 = 0 + 7

Reorder the terms:
-7 + 7 + 2n + n2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2n + n2 = 0 + 7
2n + n2 = 0 + 7

Combine like terms: 0 + 7 = 7
2n + n2 = 7

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 7 + 1

Reorder the terms:
1 + 2n + n2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + 2n + n2 = 8

Factor a perfect square on the left side:
(n + 1)(n + 1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(n + 1) equal to 2.828427125 and -2.828427125.

Subproblem 1
n + 1 = 2.828427125

Simplifying
n + 1 = 2.828427125

Reorder the terms:
1 + n = 2.828427125

Solving
1 + n = 2.828427125

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = 2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + n = 2.828427125 + -1
n = 2.828427125 + -1

Combine like terms: 2.828427125 + -1 = 1.828427125
n = 1.828427125

Simplifying
n = 1.828427125

Subproblem 2
n + 1 = -2.828427125

Simplifying
n + 1 = -2.828427125

Reorder the terms:
1 + n = -2.828427125

Solving
1 + n = -2.828427125

Solving for variable 'n'.

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

Add '-1' to each side of the equation.
1 + -1 + n = -2.828427125 + -1

Combine like terms: 1 + -1 = 0
0 + n = -2.828427125 + -1
n = -2.828427125 + -1

Combine like terms: -2.828427125 + -1 = -3.828427125
n = -3.828427125

Simplifying
n = -3.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.828427125, -3.828427125}
Solution
n = {1.828427125, -3.828427125}