3n^2+2n=33

Solution for 3n^2+2n=33 equation:

Simplifying
3n2 + 2n = 33

Reorder the terms:
2n + 3n2 = 33

Solving
2n + 3n2 = 33

Solving for variable 'n'.

Reorder the terms:
-33 + 2n + 3n2 = 33 + -33

Combine like terms: 33 + -33 = 0
-33 + 2n + 3n2 = 0

Factor a trinomial.
(-11 + -3n)(3 + -1n) = 0

Subproblem 1
Set the factor '(-11 + -3n)' equal to zero and attempt to solve:

Simplifying
-11 + -3n = 0

Solving
-11 + -3n = 0

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

Add '11' to each side of the equation.
-11 + 11 + -3n = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -3n = 0 + 11
-3n = 0 + 11

Combine like terms: 0 + 11 = 11
-3n = 11

Divide each side by '-3'.
n = -3.666666667

Simplifying
n = -3.666666667
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 = {-3.666666667, 3}