2n^2-52=5n

Solution for 2n^2-52=5n equation:

Simplifying
2n2 + -52 = 5n

Reorder the terms:
-52 + 2n2 = 5n

Solving
-52 + 2n2 = 5n

Solving for variable 'n'.

Reorder the terms:
-52 + -5n + 2n2 = 5n + -5n

Combine like terms: 5n + -5n = 0
-52 + -5n + 2n2 = 0

Factor a trinomial.
(-4 + -1n)(13 + -2n) = 0

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(13 + -2n)' equal to zero and attempt to solve:

Simplifying
13 + -2n = 0

Solving
13 + -2n = 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 + -2n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2n = 0 + -13
-2n = 0 + -13

Combine like terms: 0 + -13 = -13
-2n = -13

Divide each side by '-2'.
n = 6.5

Simplifying
n = 6.5
Solution
n = {-4, 6.5}