4n^2-26n-42=0

Solution for 4n^2-26n-42=0 equation:

Simplifying
4n2 + -26n + -42 = 0

Reorder the terms:
-42 + -26n + 4n2 = 0

Solving
-42 + -26n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -13n + 2n2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -13n + 2n2)' equal to zero and attempt to solve:

Simplifying
-21 + -13n + 2n2 = 0

Solving
-21 + -13n + 2n2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-10.5 + -6.5n + n2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -6.5n + 10.5 + n2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -6.5n + n2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -6.5n + n2 = 0 + 10.5
-6.5n + n2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-6.5n + n2 = 10.5

The n term is -6.5n.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5n + 10.5625 + n2 = 10.5 + 10.5625

Reorder the terms:
10.5625 + -6.5n + n2 = 10.5 + 10.5625

Combine like terms: 10.5 + 10.5625 = 21.0625
10.5625 + -6.5n + n2 = 21.0625

Factor a perfect square on the left side:
(n + -3.25)(n + -3.25) = 21.0625

Calculate the square root of the right side: 4.589389938

Break this problem into two subproblems by setting 
(n + -3.25) equal to 4.589389938 and -4.589389938.

Subproblem 1
n + -3.25 = 4.589389938

Simplifying
n + -3.25 = 4.589389938

Reorder the terms:
-3.25 + n = 4.589389938

Solving
-3.25 + n = 4.589389938

Solving for variable 'n'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + n = 4.589389938 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + n = 4.589389938 + 3.25
n = 4.589389938 + 3.25

Combine like terms: 4.589389938 + 3.25 = 7.839389938
n = 7.839389938

Simplifying
n = 7.839389938

Subproblem 2
n + -3.25 = -4.589389938

Simplifying
n + -3.25 = -4.589389938

Reorder the terms:
-3.25 + n = -4.589389938

Solving
-3.25 + n = -4.589389938

Solving for variable 'n'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + n = -4.589389938 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + n = -4.589389938 + 3.25
n = -4.589389938 + 3.25

Combine like terms: -4.589389938 + 3.25 = -1.339389938
n = -1.339389938

Simplifying
n = -1.339389938

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {7.839389938, -1.339389938}
Solution
n = {7.839389938, -1.339389938}