n^2-53=-5n-3

Solution for n^2-53=-5n-3 equation:

Simplifying
n2 + -53 = -5n + -3

Reorder the terms:
-53 + n2 = -5n + -3

Reorder the terms:
-53 + n2 = -3 + -5n

Solving
-53 + n2 = -3 + -5n

Solving for variable 'n'.

Reorder the terms:
-53 + 3 + 5n + n2 = -3 + -5n + 3 + 5n

Combine like terms: -53 + 3 = -50
-50 + 5n + n2 = -3 + -5n + 3 + 5n

Reorder the terms:
-50 + 5n + n2 = -3 + 3 + -5n + 5n

Combine like terms: -3 + 3 = 0
-50 + 5n + n2 = 0 + -5n + 5n
-50 + 5n + n2 = -5n + 5n

Combine like terms: -5n + 5n = 0
-50 + 5n + n2 = 0

Factor a trinomial.
(-10 + -1n)(5 + -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 '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-10, 5}