3n^2-10n+4=-2n

Solution for 3n^2-10n+4=-2n equation:

Simplifying
3n2 + -10n + 4 = -2n

Reorder the terms:
4 + -10n + 3n2 = -2n

Solving
4 + -10n + 3n2 = -2n

Solving for variable 'n'.

Reorder the terms:
4 + -10n + 2n + 3n2 = -2n + 2n

Combine like terms: -10n + 2n = -8n
4 + -8n + 3n2 = -2n + 2n

Combine like terms: -2n + 2n = 0
4 + -8n + 3n2 = 0

Factor a trinomial.
(2 + -3n)(2 + -1n) = 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 '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {0.6666666667, 2}