2(n-3)+n(2-n)=2-n^2

Solution for 2(n-3)+n(2-n)=2-n^2 equation:

Simplifying
2(n + -3) + n(2 + -1n) = 2 + -1n2

Reorder the terms:
2(-3 + n) + n(2 + -1n) = 2 + -1n2
(-3 * 2 + n * 2) + n(2 + -1n) = 2 + -1n2
(-6 + 2n) + n(2 + -1n) = 2 + -1n2
-6 + 2n + (2 * n + -1n * n) = 2 + -1n2
-6 + 2n + (2n + -1n2) = 2 + -1n2

Combine like terms: 2n + 2n = 4n
-6 + 4n + -1n2 = 2 + -1n2

Add 'n2' to each side of the equation.
-6 + 4n + -1n2 + n2 = 2 + -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-6 + 4n + 0 = 2 + -1n2 + n2
-6 + 4n = 2 + -1n2 + n2

Combine like terms: -1n2 + n2 = 0
-6 + 4n = 2 + 0
-6 + 4n = 2

Solving
-6 + 4n = 2

Solving for variable 'n'.

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

Add '6' to each side of the equation.
-6 + 6 + 4n = 2 + 6

Combine like terms: -6 + 6 = 0
0 + 4n = 2 + 6
4n = 2 + 6

Combine like terms: 2 + 6 = 8
4n = 8

Divide each side by '4'.
n = 2

Simplifying
n = 2