5n^2-6=2n-5

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

Simplifying
5n2 + -6 = 2n + -5

Reorder the terms:
-6 + 5n2 = 2n + -5

Reorder the terms:
-6 + 5n2 = -5 + 2n

Solving
-6 + 5n2 = -5 + 2n

Solving for variable 'n'.

Reorder the terms:
-6 + 5 + -2n + 5n2 = -5 + 2n + 5 + -2n

Combine like terms: -6 + 5 = -1
-1 + -2n + 5n2 = -5 + 2n + 5 + -2n

Reorder the terms:
-1 + -2n + 5n2 = -5 + 5 + 2n + -2n

Combine like terms: -5 + 5 = 0
-1 + -2n + 5n2 = 0 + 2n + -2n
-1 + -2n + 5n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-1 + -2n + 5n2 = 0

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

Divide each side by '5'.
-0.2 + -0.4n + n2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -0.4n + 0.2 + n2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -0.4n + n2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -0.4n + n2 = 0 + 0.2
-0.4n + n2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-0.4n + n2 = 0.2

The n term is -0.4n.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4n + 0.04 + n2 = 0.2 + 0.04

Reorder the terms:
0.04 + -0.4n + n2 = 0.2 + 0.04

Combine like terms: 0.2 + 0.04 = 0.24
0.04 + -0.4n + n2 = 0.24

Factor a perfect square on the left side:
(n + -0.2)(n + -0.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(n + -0.2) equal to 0.489897949 and -0.489897949.

Subproblem 1
n + -0.2 = 0.489897949

Simplifying
n + -0.2 = 0.489897949

Reorder the terms:
-0.2 + n = 0.489897949

Solving
-0.2 + n = 0.489897949

Solving for variable 'n'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + n = 0.489897949 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + n = 0.489897949 + 0.2
n = 0.489897949 + 0.2

Combine like terms: 0.489897949 + 0.2 = 0.689897949
n = 0.689897949

Simplifying
n = 0.689897949

Subproblem 2
n + -0.2 = -0.489897949

Simplifying
n + -0.2 = -0.489897949

Reorder the terms:
-0.2 + n = -0.489897949

Solving
-0.2 + n = -0.489897949

Solving for variable 'n'.

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

Add '0.2' to each side of the equation.
-0.2 + 0.2 + n = -0.489897949 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + n = -0.489897949 + 0.2
n = -0.489897949 + 0.2

Combine like terms: -0.489897949 + 0.2 = -0.289897949
n = -0.289897949

Simplifying
n = -0.289897949

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {0.689897949, -0.289897949}