35n^2-8n-42=-n

Solution for 35n^2-8n-42=-n equation:

Simplifying
35n2 + -8n + -42 = -1n

Reorder the terms:
-42 + -8n + 35n2 = -1n

Solving
-42 + -8n + 35n2 = -1n

Solving for variable 'n'.

Reorder the terms:
-42 + -8n + n + 35n2 = -1n + n

Combine like terms: -8n + n = -7n
-42 + -7n + 35n2 = -1n + n

Combine like terms: -1n + n = 0
-42 + -7n + 35n2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + -1n + 5n2) = 0

Factor a trinomial.
7((-1 + -1n)(6 + -5n)) = 0

Ignore the factor 7.
Subproblem 1
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
Subproblem 2
Set the factor '(6 + -5n)' equal to zero and attempt to solve:

Simplifying
6 + -5n = 0

Solving
6 + -5n = 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 + -5n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5n = 0 + -6
-5n = 0 + -6

Combine like terms: 0 + -6 = -6
-5n = -6

Divide each side by '-5'.
n = 1.2

Simplifying
n = 1.2
Solution
n = {-1, 1.2}