-3n(n+1)=2-4(n+1)

Solution for -3n(n+1)=2-4(n+1) equation:

Simplifying
-3n(n + 1) = 2 + -4(n + 1)

Reorder the terms:
-3n(1 + n) = 2 + -4(n + 1)
(1 * -3n + n * -3n) = 2 + -4(n + 1)
(-3n + -3n2) = 2 + -4(n + 1)

Reorder the terms:
-3n + -3n2 = 2 + -4(1 + n)
-3n + -3n2 = 2 + (1 * -4 + n * -4)
-3n + -3n2 = 2 + (-4 + -4n)

Combine like terms: 2 + -4 = -2
-3n + -3n2 = -2 + -4n

Solving
-3n + -3n2 = -2 + -4n

Solving for variable 'n'.

Reorder the terms:
2 + -3n + 4n + -3n2 = -2 + -4n + 2 + 4n

Combine like terms: -3n + 4n = 1n
2 + 1n + -3n2 = -2 + -4n + 2 + 4n

Reorder the terms:
2 + 1n + -3n2 = -2 + 2 + -4n + 4n

Combine like terms: -2 + 2 = 0
2 + 1n + -3n2 = 0 + -4n + 4n
2 + 1n + -3n2 = -4n + 4n

Combine like terms: -4n + 4n = 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}