42n^2-n-30=0

Solution for 42n^2-n-30=0 equation:

Simplifying
42n2 + -1n + -30 = 0

Reorder the terms:
-30 + -1n + 42n2 = 0

Solving
-30 + -1n + 42n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -6n = 0

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

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

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

Divide each side by '-6'.
n = -0.8333333333

Simplifying
n = -0.8333333333
Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 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 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Solution
n = {-0.8333333333, 0.8571428571}