n^2+5n-6=42

Solution for n^2+5n-6=42 equation:

Simplifying
n2 + 5n + -6 = 42

Reorder the terms:
-6 + 5n + n2 = 42

Solving
-6 + 5n + n2 = 42

Solving for variable 'n'.

Reorder the terms:
-6 + -42 + 5n + n2 = 42 + -42

Combine like terms: -6 + -42 = -48
-48 + 5n + n2 = 42 + -42

Combine like terms: 42 + -42 = 0
-48 + 5n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '48' to each side of the equation.
-48 + 5n + 48 + n2 = 0 + 48

Reorder the terms:
-48 + 48 + 5n + n2 = 0 + 48

Combine like terms: -48 + 48 = 0
0 + 5n + n2 = 0 + 48
5n + n2 = 0 + 48

Combine like terms: 0 + 48 = 48
5n + n2 = 48

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = 48 + 6.25

Reorder the terms:
6.25 + 5n + n2 = 48 + 6.25

Combine like terms: 48 + 6.25 = 54.25
6.25 + 5n + n2 = 54.25

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 54.25

Calculate the square root of the right side: 7.365459931

Break this problem into two subproblems by setting 
(n + 2.5) equal to 7.365459931 and -7.365459931.

Subproblem 1
n + 2.5 = 7.365459931

Simplifying
n + 2.5 = 7.365459931

Reorder the terms:
2.5 + n = 7.365459931

Solving
2.5 + n = 7.365459931

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = 7.365459931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = 7.365459931 + -2.5
n = 7.365459931 + -2.5

Combine like terms: 7.365459931 + -2.5 = 4.865459931
n = 4.865459931

Simplifying
n = 4.865459931

Subproblem 2
n + 2.5 = -7.365459931

Simplifying
n + 2.5 = -7.365459931

Reorder the terms:
2.5 + n = -7.365459931

Solving
2.5 + n = -7.365459931

Solving for variable 'n'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + n = -7.365459931 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + n = -7.365459931 + -2.5
n = -7.365459931 + -2.5

Combine like terms: -7.365459931 + -2.5 = -9.865459931
n = -9.865459931

Simplifying
n = -9.865459931

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {4.865459931, -9.865459931}