5n^2-23n=10

Solution for 5n^2-23n=10 equation:

Simplifying
5n2 + -23n = 10

Reorder the terms:
-23n + 5n2 = 10

Solving
-23n + 5n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + -23n + 5n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -23n + 5n2 = 0

Factor a trinomial.
(-2 + -5n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve:

Simplifying
-2 + -5n = 0

Solving
-2 + -5n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5n = 0 + 2

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

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

Divide each side by '-5'.
n = -0.4

Simplifying
n = -0.4
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 = {-0.4, 5}