6n*n+4n=10

Solution for 6n*n+4n=10 equation:

Simplifying
6n * n + 4n = 10

Multiply n * n
6n2 + 4n = 10

Reorder the terms:
4n + 6n2 = 10

Solving
4n + 6n2 = 10

Solving for variable 'n'.

Reorder the terms:
-10 + 4n + 6n2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 4n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 2n + 3n2) = 0

Factor a trinomial.
2((-5 + -3n)(1 + -1n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -3n)' equal to zero and attempt to solve:

Simplifying
-5 + -3n = 0

Solving
-5 + -3n = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3n = 0 + 5
-3n = 0 + 5

Combine like terms: 0 + 5 = 5
-3n = 5

Divide each side by '-3'.
n = -1.666666667

Simplifying
n = -1.666666667
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 = {-1.666666667, 1}