3n^2-9n=-2n+6

Solution for 3n^2-9n=-2n+6 equation:

Simplifying
3n2 + -9n = -2n + 6

Reorder the terms:
-9n + 3n2 = -2n + 6

Reorder the terms:
-9n + 3n2 = 6 + -2n

Solving
-9n + 3n2 = 6 + -2n

Solving for variable 'n'.

Reorder the terms:
-6 + -9n + 2n + 3n2 = 6 + -2n + -6 + 2n

Combine like terms: -9n + 2n = -7n
-6 + -7n + 3n2 = 6 + -2n + -6 + 2n

Reorder the terms:
-6 + -7n + 3n2 = 6 + -6 + -2n + 2n

Combine like terms: 6 + -6 = 0
-6 + -7n + 3n2 = 0 + -2n + 2n
-6 + -7n + 3n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
-6 + -7n + 3n2 = 0

Factor a trinomial.
(-2 + -3n)(3 + -1n) = 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 '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

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

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

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {-0.6666666667, 3}