15n(n+1)=2n-2

Solution for 15n(n+1)=2n-2 equation:

Simplifying
15n(n + 1) = 2n + -2

Reorder the terms:
15n(1 + n) = 2n + -2
(1 * 15n + n * 15n) = 2n + -2
(15n + 15n2) = 2n + -2

Reorder the terms:
15n + 15n2 = -2 + 2n

Solving
15n + 15n2 = -2 + 2n

Solving for variable 'n'.

Reorder the terms:
2 + 15n + -2n + 15n2 = -2 + 2n + 2 + -2n

Combine like terms: 15n + -2n = 13n
2 + 13n + 15n2 = -2 + 2n + 2 + -2n

Reorder the terms:
2 + 13n + 15n2 = -2 + 2 + 2n + -2n

Combine like terms: -2 + 2 = 0
2 + 13n + 15n2 = 0 + 2n + -2n
2 + 13n + 15n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
2 + 13n + 15n2 = 0

Factor a trinomial.
(2 + 3n)(1 + 5n) = 0

Subproblem 1
Set the factor '(2 + 3n)' equal to zero and attempt to solve:

Simplifying
2 + 3n = 0

Solving
2 + 3n = 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 + 3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3n = 0 + -2
3n = 0 + -2

Combine like terms: 0 + -2 = -2
3n = -2

Divide each side by '3'.
n = -0.6666666667

Simplifying
n = -0.6666666667
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 = {-0.6666666667, -0.2}