10n(n+3)=3n-5

Solution for 10n(n+3)=3n-5 equation:

Simplifying
10n(n + 3) = 3n + -5

Reorder the terms:
10n(3 + n) = 3n + -5
(3 * 10n + n * 10n) = 3n + -5
(30n + 10n2) = 3n + -5

Reorder the terms:
30n + 10n2 = -5 + 3n

Solving
30n + 10n2 = -5 + 3n

Solving for variable 'n'.

Reorder the terms:
5 + 30n + -3n + 10n2 = -5 + 3n + 5 + -3n

Combine like terms: 30n + -3n = 27n
5 + 27n + 10n2 = -5 + 3n + 5 + -3n

Reorder the terms:
5 + 27n + 10n2 = -5 + 5 + 3n + -3n

Combine like terms: -5 + 5 = 0
5 + 27n + 10n2 = 0 + 3n + -3n
5 + 27n + 10n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
5 + 27n + 10n2 = 0

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

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

Simplifying
5 + 2n = 0

Solving
5 + 2n = 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 + 2n = 0 + -5

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

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

Divide each side by '2'.
n = -2.5

Simplifying
n = -2.5
Subproblem 2
Set the factor '(1 + 5n)' equal to zero and attempt to solve:

Simplifying
1 + 5n = 0

Solving
1 + 5n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5n = 0 + -1
5n = 0 + -1

Combine like terms: 0 + -1 = -1
5n = -1

Divide each side by '5'.
n = -0.2

Simplifying
n = -0.2
Solution
n = {-2.5, -0.2}