2n^2+19n-1=6+6n

Solution for 2n^2+19n-1=6+6n equation:

Simplifying
2n2 + 19n + -1 = 6 + 6n

Reorder the terms:
-1 + 19n + 2n2 = 6 + 6n

Solving
-1 + 19n + 2n2 = 6 + 6n

Solving for variable 'n'.

Reorder the terms:
-1 + -6 + 19n + -6n + 2n2 = 6 + 6n + -6 + -6n

Combine like terms: -1 + -6 = -7
-7 + 19n + -6n + 2n2 = 6 + 6n + -6 + -6n

Combine like terms: 19n + -6n = 13n
-7 + 13n + 2n2 = 6 + 6n + -6 + -6n

Reorder the terms:
-7 + 13n + 2n2 = 6 + -6 + 6n + -6n

Combine like terms: 6 + -6 = 0
-7 + 13n + 2n2 = 0 + 6n + -6n
-7 + 13n + 2n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-7 + 13n + 2n2 = 0

Factor a trinomial.
(-7 + -1n)(1 + -2n) = 0

Subproblem 1
Set the factor '(-7 + -1n)' equal to zero and attempt to solve:

Simplifying
-7 + -1n = 0

Solving
-7 + -1n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1n = 0 + 7
-1n = 0 + 7

Combine like terms: 0 + 7 = 7
-1n = 7

Divide each side by '-1'.
n = -7

Simplifying
n = -7
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 = {-7, 0.5}