(2n-1)(2n-1)+4(2n-1)-12=0

Solution for (2n-1)(2n-1)+4(2n-1)-12=0 equation:

Simplifying
(2n + -1)(2n + -1) + 4(2n + -1) + -12 = 0

Reorder the terms:
(-1 + 2n)(2n + -1) + 4(2n + -1) + -12 = 0

Reorder the terms:
(-1 + 2n)(-1 + 2n) + 4(2n + -1) + -12 = 0

Multiply (-1 + 2n) * (-1 + 2n)
(-1(-1 + 2n) + 2n * (-1 + 2n)) + 4(2n + -1) + -12 = 0
((-1 * -1 + 2n * -1) + 2n * (-1 + 2n)) + 4(2n + -1) + -12 = 0
((1 + -2n) + 2n * (-1 + 2n)) + 4(2n + -1) + -12 = 0
(1 + -2n + (-1 * 2n + 2n * 2n)) + 4(2n + -1) + -12 = 0
(1 + -2n + (-2n + 4n2)) + 4(2n + -1) + -12 = 0

Combine like terms: -2n + -2n = -4n
(1 + -4n + 4n2) + 4(2n + -1) + -12 = 0

Reorder the terms:
1 + -4n + 4n2 + 4(-1 + 2n) + -12 = 0
1 + -4n + 4n2 + (-1 * 4 + 2n * 4) + -12 = 0
1 + -4n + 4n2 + (-4 + 8n) + -12 = 0

Reorder the terms:
1 + -4 + -12 + -4n + 8n + 4n2 = 0

Combine like terms: 1 + -4 = -3
-3 + -12 + -4n + 8n + 4n2 = 0

Combine like terms: -3 + -12 = -15
-15 + -4n + 8n + 4n2 = 0

Combine like terms: -4n + 8n = 4n
-15 + 4n + 4n2 = 0

Solving
-15 + 4n + 4n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -2n)(3 + -2n) = 0

Subproblem 1
Set the factor '(-5 + -2n)' equal to zero and attempt to solve:

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -2n = 0 + 5

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

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

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(3 + -2n)' equal to zero and attempt to solve:

Simplifying
3 + -2n = 0

Solving
3 + -2n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2n = 0 + -3
-2n = 0 + -3

Combine like terms: 0 + -3 = -3
-2n = -3

Divide each side by '-2'.
n = 1.5

Simplifying
n = 1.5
Solution
n = {-2.5, 1.5}