6n^2-3n-5+10n=0

Solution for 6n^2-3n-5+10n=0 equation:

Simplifying
6n2 + -3n + -5 + 10n = 0

Reorder the terms:
-5 + -3n + 10n + 6n2 = 0

Combine like terms: -3n + 10n = 7n
-5 + 7n + 6n2 = 0

Solving
-5 + 7n + 6n2 = 0

Solving for variable 'n'.

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

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 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

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

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

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

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {-1.666666667, 0.5}