25n^2=24+10n

Solution for 25n^2=24+10n equation:

Simplifying
25n2 = 24 + 10n

Solving
25n2 = 24 + 10n

Solving for variable 'n'.

Reorder the terms:
-24 + -10n + 25n2 = 24 + 10n + -24 + -10n

Reorder the terms:
-24 + -10n + 25n2 = 24 + -24 + 10n + -10n

Combine like terms: 24 + -24 = 0
-24 + -10n + 25n2 = 0 + 10n + -10n
-24 + -10n + 25n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-24 + -10n + 25n2 = 0

Factor a trinomial.
(-4 + -5n)(6 + -5n) = 0

Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve:

Simplifying
-4 + -5n = 0

Solving
-4 + -5n = 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 + -5n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5n = 0 + 4
-5n = 0 + 4

Combine like terms: 0 + 4 = 4
-5n = 4

Divide each side by '-5'.
n = -0.8

Simplifying
n = -0.8
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-0.8, 1.2}