n^2+4(n+1)=64

Solution for n^2+4(n+1)=64 equation:

Simplifying
n2 + 4(n + 1) = 64

Reorder the terms:
n2 + 4(1 + n) = 64
n2 + (1 * 4 + n * 4) = 64
n2 + (4 + 4n) = 64

Reorder the terms:
4 + 4n + n2 = 64

Solving
4 + 4n + n2 = 64

Solving for variable 'n'.

Reorder the terms:
4 + -64 + 4n + n2 = 64 + -64

Combine like terms: 4 + -64 = -60
-60 + 4n + n2 = 64 + -64

Combine like terms: 64 + -64 = 0
-60 + 4n + n2 = 0

Factor a trinomial.
(-10 + -1n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-10 + -1n)' equal to zero and attempt to solve:

Simplifying
-10 + -1n = 0

Solving
-10 + -1n = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1n = 0 + 10
-1n = 0 + 10

Combine like terms: 0 + 10 = 10
-1n = 10

Divide each side by '-1'.
n = -10

Simplifying
n = -10
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-10, 6}