15n^2+19n+6=10+2n

Solution for 15n^2+19n+6=10+2n equation:

Simplifying
15n2 + 19n + 6 = 10 + 2n

Reorder the terms:
6 + 19n + 15n2 = 10 + 2n

Solving
6 + 19n + 15n2 = 10 + 2n

Solving for variable 'n'.

Reorder the terms:
6 + -10 + 19n + -2n + 15n2 = 10 + 2n + -10 + -2n

Combine like terms: 6 + -10 = -4
-4 + 19n + -2n + 15n2 = 10 + 2n + -10 + -2n

Combine like terms: 19n + -2n = 17n
-4 + 17n + 15n2 = 10 + 2n + -10 + -2n

Reorder the terms:
-4 + 17n + 15n2 = 10 + -10 + 2n + -2n

Combine like terms: 10 + -10 = 0
-4 + 17n + 15n2 = 0 + 2n + -2n
-4 + 17n + 15n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
-4 + 17n + 15n2 = 0

Factor a trinomial.
(-4 + -3n)(1 + -5n) = 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 + -5n)' equal to zero and attempt to solve:

Simplifying
1 + -5n = 0

Solving
1 + -5n = 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 + -5n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5n = 0 + -1
-5n = 0 + -1

Combine like terms: 0 + -1 = -1
-5n = -1

Divide each side by '-5'.
n = 0.2

Simplifying
n = 0.2
Solution
n = {-1.333333333, 0.2}