n(3n-10)=25

Solution for n(3n-10)=25 equation:

Simplifying
n(3n + -10) = 25

Reorder the terms:
n(-10 + 3n) = 25
(-10 * n + 3n * n) = 25
(-10n + 3n2) = 25

Solving
-10n + 3n2 = 25

Solving for variable 'n'.

Reorder the terms:
-25 + -10n + 3n2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -10n + 3n2 = 0

Factor a trinomial.
(-5 + -3n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve:

Simplifying
-5 + -3n = 0

Solving
-5 + -3n = 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 + -3n = 0 + 5

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

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

Divide each side by '-3'.
n = -1.666666667

Simplifying
n = -1.666666667
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 = {-1.666666667, 5}