3n^2=2n+33

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

Simplifying
3n2 = 2n + 33

Reorder the terms:
3n2 = 33 + 2n

Solving
3n2 = 33 + 2n

Solving for variable 'n'.

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

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

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-3, 3.666666667}