42n^2+36n-6=0

Solution for 42n^2+36n-6=0 equation:

Simplifying
42n2 + 36n + -6 = 0

Reorder the terms:
-6 + 36n + 42n2 = 0

Solving
-6 + 36n + 42n2 = 0

Solving for variable 'n'.

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

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

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

Simplifying
1 + -7n = 0

Solving
1 + -7n = 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 + -7n = 0 + -1

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

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

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Solution
n = {-1, 0.1428571429}