3n^2=-n+4

Solution for 3n^2=-n+4 equation:

Simplifying
3n2 = -1n + 4

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

Solving
3n2 = 4 + -1n

Solving for variable 'n'.

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

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

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

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

Factor a trinomial.
(-4 + -3n)(1 + -1n) = 0

Subproblem 1
Set the factor '(-4 + -3n)' equal to zero and attempt to solve:

Simplifying
-4 + -3n = 0

Solving
-4 + -3n = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3n = 0 + 4
-3n = 0 + 4

Combine like terms: 0 + 4 = 4
-3n = 4

Divide each side by '-3'.
n = -1.333333333

Simplifying
n = -1.333333333
Subproblem 2
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
Solution
n = {-1.333333333, 1}