3n(n+1)=2(n+1)

Solution for 3n(n+1)=2(n+1) equation:

Simplifying
3n(n + 1) = 2(n + 1)

Reorder the terms:
3n(1 + n) = 2(n + 1)
(1 * 3n + n * 3n) = 2(n + 1)
(3n + 3n2) = 2(n + 1)

Reorder the terms:
3n + 3n2 = 2(1 + n)
3n + 3n2 = (1 * 2 + n * 2)
3n + 3n2 = (2 + 2n)

Solving
3n + 3n2 = 2 + 2n

Solving for variable 'n'.

Reorder the terms:
-2 + 3n + -2n + 3n2 = 2 + 2n + -2 + -2n

Combine like terms: 3n + -2n = 1n
-2 + 1n + 3n2 = 2 + 2n + -2 + -2n

Reorder the terms:
-2 + 1n + 3n2 = 2 + -2 + 2n + -2n

Combine like terms: 2 + -2 = 0
-2 + 1n + 3n2 = 0 + 2n + -2n
-2 + 1n + 3n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-2 + 1n + 3n2 = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 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 + -1n = 0 + 1

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

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

Divide each side by '-1'.
n = -1

Simplifying
n = -1
Subproblem 2
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
Solution
n = {-1, 0.6666666667}