n^2+10n+25=64

Solution for n^2+10n+25=64 equation:

Simplifying
n2 + 10n + 25 = 64

Reorder the terms:
25 + 10n + n2 = 64

Solving
25 + 10n + n2 = 64

Solving for variable 'n'.

Reorder the terms:
25 + -64 + 10n + n2 = 64 + -64

Combine like terms: 25 + -64 = -39
-39 + 10n + n2 = 64 + -64

Combine like terms: 64 + -64 = 0
-39 + 10n + n2 = 0

Factor a trinomial.
(-13 + -1n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -1n)' equal to zero and attempt to solve:

Simplifying
-13 + -1n = 0

Solving
-13 + -1n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1n = 0 + 13
-1n = 0 + 13

Combine like terms: 0 + 13 = 13
-1n = 13

Divide each side by '-1'.
n = -13

Simplifying
n = -13
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-13, 3}