-6n^2+17n+42=-8n^2-2n

Solution for -6n^2+17n+42=-8n^2-2n equation:

Simplifying
-6n2 + 17n + 42 = -8n2 + -2n

Reorder the terms:
42 + 17n + -6n2 = -8n2 + -2n

Reorder the terms:
42 + 17n + -6n2 = -2n + -8n2

Solving
42 + 17n + -6n2 = -2n + -8n2

Solving for variable 'n'.

Reorder the terms:
42 + 17n + 2n + -6n2 + 8n2 = -2n + -8n2 + 2n + 8n2

Combine like terms: 17n + 2n = 19n
42 + 19n + -6n2 + 8n2 = -2n + -8n2 + 2n + 8n2

Combine like terms: -6n2 + 8n2 = 2n2
42 + 19n + 2n2 = -2n + -8n2 + 2n + 8n2

Reorder the terms:
42 + 19n + 2n2 = -2n + 2n + -8n2 + 8n2

Combine like terms: -2n + 2n = 0
42 + 19n + 2n2 = 0 + -8n2 + 8n2
42 + 19n + 2n2 = -8n2 + 8n2

Combine like terms: -8n2 + 8n2 = 0
42 + 19n + 2n2 = 0

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

Subproblem 1
Set the factor '(6 + n)' equal to zero and attempt to solve:

Simplifying
6 + n = 0

Solving
6 + n = 0

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

Add '-6' to each side of the equation.
6 + -6 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(7 + 2n)' equal to zero and attempt to solve:

Simplifying
7 + 2n = 0

Solving
7 + 2n = 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 + 2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2n = 0 + -7
2n = 0 + -7

Combine like terms: 0 + -7 = -7
2n = -7

Divide each side by '2'.
n = -3.5

Simplifying
n = -3.5
Solution
n = {-6, -3.5}