42n^2-258n-252=0

Solution for 42n^2-258n-252=0 equation:

Simplifying
42n2 + -258n + -252 = 0

Reorder the terms:
-252 + -258n + 42n2 = 0

Solving
-252 + -258n + 42n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-42 + -43n + 7n2) = 0

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

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
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
Solution
n = {-0.8571428571, 7}