2n^2+4n-60=0

Solution for 2n^2+4n-60=0 equation:

Simplifying
2n2 + 4n + -60 = 0

Reorder the terms:
-60 + 4n + 2n2 = 0

Solving
-60 + 4n + 2n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 2n + n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-30 + 2n + n2)' equal to zero and attempt to solve:

Simplifying
-30 + 2n + n2 = 0

Solving
-30 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2n + 30 + n2 = 0 + 30

Reorder the terms:
-30 + 30 + 2n + n2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2n + n2 = 0 + 30
2n + n2 = 0 + 30

Combine like terms: 0 + 30 = 30
2n + n2 = 30

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 = 30 + 1

Reorder the terms:
1 + 2n + n2 = 30 + 1

Combine like terms: 30 + 1 = 31
1 + 2n + n2 = 31

Factor a perfect square on the left side:
(n + 1)(n + 1) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(n + 1) equal to 5.567764363 and -5.567764363.

Subproblem 1
n + 1 = 5.567764363

Simplifying
n + 1 = 5.567764363

Reorder the terms:
1 + n = 5.567764363

Solving
1 + n = 5.567764363

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 = 5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + n = 5.567764363 + -1
n = 5.567764363 + -1

Combine like terms: 5.567764363 + -1 = 4.567764363
n = 4.567764363

Simplifying
n = 4.567764363

Subproblem 2
n + 1 = -5.567764363

Simplifying
n + 1 = -5.567764363

Reorder the terms:
1 + n = -5.567764363

Solving
1 + n = -5.567764363

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 = -5.567764363 + -1

Combine like terms: 1 + -1 = 0
0 + n = -5.567764363 + -1
n = -5.567764363 + -1

Combine like terms: -5.567764363 + -1 = -6.567764363
n = -6.567764363

Simplifying
n = -6.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.567764363, -6.567764363}
Solution
n = {4.567764363, -6.567764363}