3n^2-2n+1=-3n^2+9n+11

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Solution for 3n^2-2n+1=-3n^2+9n+11 equation: 


Simplifying
3n2 + -2n + 1 = -3n2 + 9n + 11

Reorder the terms:
1 + -2n + 3n2 = -3n2 + 9n + 11

Reorder the terms:
1 + -2n + 3n2 = 11 + 9n + -3n2

Solving
1 + -2n + 3n2 = 11 + 9n + -3n2

Solving for variable 'n'.

Reorder the terms:
1 + -11 + -2n + -9n + 3n2 + 3n2 = 11 + 9n + -3n2 + -11 + -9n + 3n2

Combine like terms: 1 + -11 = -10
-10 + -2n + -9n + 3n2 + 3n2 = 11 + 9n + -3n2 + -11 + -9n + 3n2

Combine like terms: -2n + -9n = -11n
-10 + -11n + 3n2 + 3n2 = 11 + 9n + -3n2 + -11 + -9n + 3n2

Combine like terms: 3n2 + 3n2 = 6n2
-10 + -11n + 6n2 = 11 + 9n + -3n2 + -11 + -9n + 3n2

Reorder the terms:
-10 + -11n + 6n2 = 11 + -11 + 9n + -9n + -3n2 + 3n2

Combine like terms: 11 + -11 = 0
-10 + -11n + 6n2 = 0 + 9n + -9n + -3n2 + 3n2
-10 + -11n + 6n2 = 9n + -9n + -3n2 + 3n2

Combine like terms: 9n + -9n = 0
-10 + -11n + 6n2 = 0 + -3n2 + 3n2
-10 + -11n + 6n2 = -3n2 + 3n2

Combine like terms: -3n2 + 3n2 = 0
-10 + -11n + 6n2 = 0

Factor a trinomial.
(-2 + -3n)(5 + -2n) = 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 '(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
Solution
n = {-0.6666666667, 2.5}

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