(2n-2)5n-(2n-3)(n-2)=

Solution for (2n-2)5n-(2n-3)(n-2)= equation:

Simplifying
(2n + -2) * 5n + -1(2n + -3)(n + -2) = 0

Reorder the terms:
(-2 + 2n) * 5n + -1(2n + -3)(n + -2) = 0

Reorder the terms for easier multiplication:
5n(-2 + 2n) + -1(2n + -3)(n + -2) = 0
(-2 * 5n + 2n * 5n) + -1(2n + -3)(n + -2) = 0
(-10n + 10n2) + -1(2n + -3)(n + -2) = 0

Reorder the terms:
-10n + 10n2 + -1(-3 + 2n)(n + -2) = 0

Reorder the terms:
-10n + 10n2 + -1(-3 + 2n)(-2 + n) = 0

Multiply (-3 + 2n) * (-2 + n)
-10n + 10n2 + -1(-3(-2 + n) + 2n * (-2 + n)) = 0
-10n + 10n2 + -1((-2 * -3 + n * -3) + 2n * (-2 + n)) = 0
-10n + 10n2 + -1((6 + -3n) + 2n * (-2 + n)) = 0
-10n + 10n2 + -1(6 + -3n + (-2 * 2n + n * 2n)) = 0
-10n + 10n2 + -1(6 + -3n + (-4n + 2n2)) = 0

Combine like terms: -3n + -4n = -7n
-10n + 10n2 + -1(6 + -7n + 2n2) = 0
-10n + 10n2 + (6 * -1 + -7n * -1 + 2n2 * -1) = 0
-10n + 10n2 + (-6 + 7n + -2n2) = 0

Reorder the terms:
-6 + -10n + 7n + 10n2 + -2n2 = 0

Combine like terms: -10n + 7n = -3n
-6 + -3n + 10n2 + -2n2 = 0

Combine like terms: 10n2 + -2n2 = 8n2
-6 + -3n + 8n2 = 0

Solving
-6 + -3n + 8n2 = 0

Solving for variable 'n'.

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

Divide each side by '8'.
-0.75 + -0.375n + n2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.375n + 0.75 + n2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.375n + n2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.375n + n2 = 0 + 0.75
-0.375n + n2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.375n + n2 = 0.75

The n term is -0.375n.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375n + 0.03515625 + n2 = 0.75 + 0.03515625

Reorder the terms:
0.03515625 + -0.375n + n2 = 0.75 + 0.03515625

Combine like terms: 0.75 + 0.03515625 = 0.78515625
0.03515625 + -0.375n + n2 = 0.78515625

Factor a perfect square on the left side:
(n + -0.1875)(n + -0.1875) = 0.78515625

Calculate the square root of the right side: 0.88609043

Break this problem into two subproblems by setting 
(n + -0.1875) equal to 0.88609043 and -0.88609043.

Subproblem 1
n + -0.1875 = 0.88609043

Simplifying
n + -0.1875 = 0.88609043

Reorder the terms:
-0.1875 + n = 0.88609043

Solving
-0.1875 + n = 0.88609043

Solving for variable 'n'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + n = 0.88609043 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + n = 0.88609043 + 0.1875
n = 0.88609043 + 0.1875

Combine like terms: 0.88609043 + 0.1875 = 1.07359043
n = 1.07359043

Simplifying
n = 1.07359043

Subproblem 2
n + -0.1875 = -0.88609043

Simplifying
n + -0.1875 = -0.88609043

Reorder the terms:
-0.1875 + n = -0.88609043

Solving
-0.1875 + n = -0.88609043

Solving for variable 'n'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + n = -0.88609043 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + n = -0.88609043 + 0.1875
n = -0.88609043 + 0.1875

Combine like terms: -0.88609043 + 0.1875 = -0.69859043
n = -0.69859043

Simplifying
n = -0.69859043

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {1.07359043, -0.69859043}