0=42n^2+192n-360

Solution for 0=42n^2+192n-360 equation:

Simplifying
0 = 42n2 + 192n + -360

Reorder the terms:
0 = -360 + 192n + 42n2

Solving
0 = -360 + 192n + 42n2

Solving for variable 'n'.

Combine like terms: 0 + 360 = 360
360 + -192n + -42n2 = -360 + 192n + 42n2 + 360 + -192n + -42n2

Reorder the terms:
360 + -192n + -42n2 = -360 + 360 + 192n + -192n + 42n2 + -42n2

Combine like terms: -360 + 360 = 0
360 + -192n + -42n2 = 0 + 192n + -192n + 42n2 + -42n2
360 + -192n + -42n2 = 192n + -192n + 42n2 + -42n2

Combine like terms: 192n + -192n = 0
360 + -192n + -42n2 = 0 + 42n2 + -42n2
360 + -192n + -42n2 = 42n2 + -42n2

Combine like terms: 42n2 + -42n2 = 0
360 + -192n + -42n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(60 + -32n + -7n2) = 0

Factor a trinomial.
6((10 + -7n)(6 + n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(10 + -7n)' equal to zero and attempt to solve:

Simplifying
10 + -7n = 0

Solving
10 + -7n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -7n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -7n = 0 + -10
-7n = 0 + -10

Combine like terms: 0 + -10 = -10
-7n = -10

Divide each side by '-7'.
n = 1.428571429

Simplifying
n = 1.428571429
Subproblem 2
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
Solution
n = {1.428571429, -6}