3n^2=4n-1

Solution for 3n^2=4n-1 equation:

Simplifying
3n2 = 4n + -1

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

Solving
3n2 = -1 + 4n

Solving for variable 'n'.

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

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

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

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

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

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

Simplifying
1 + -3n = 0

Solving
1 + -3n = 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 + -3n = 0 + -1

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

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

Divide each side by '-3'.
n = 0.3333333333

Simplifying
n = 0.3333333333
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 = {0.3333333333, 1}