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.
(-5 + -1n)(2 + -5n) = 0

Subproblem 1
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
Subproblem 2
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
Solution
n = {-5, 0.4}