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

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

Simplifying
(n + -1) * 2 + 4n = (n + 1) * 2

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

Reorder the terms for easier multiplication:
2(-1 + n) + 4n = (n + 1) * 2
(-1 * 2 + n * 2) + 4n = (n + 1) * 2
(-2 + 2n) + 4n = (n + 1) * 2

Combine like terms: 2n + 4n = 6n
-2 + 6n = (n + 1) * 2

Reorder the terms:
-2 + 6n = (1 + n) * 2

Reorder the terms for easier multiplication:
-2 + 6n = 2(1 + n)
-2 + 6n = (1 * 2 + n * 2)
-2 + 6n = (2 + 2n)

Solving
-2 + 6n = 2 + 2n

Solving for variable 'n'.

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

Add '-2n' to each side of the equation.
-2 + 6n + -2n = 2 + 2n + -2n

Combine like terms: 6n + -2n = 4n
-2 + 4n = 2 + 2n + -2n

Combine like terms: 2n + -2n = 0
-2 + 4n = 2 + 0
-2 + 4n = 2

Add '2' to each side of the equation.
-2 + 2 + 4n = 2 + 2

Combine like terms: -2 + 2 = 0
0 + 4n = 2 + 2
4n = 2 + 2

Combine like terms: 2 + 2 = 4
4n = 4

Divide each side by '4'.
n = 1

Simplifying
n = 1