6n^2+2n-140=0

Solution for 6n^2+2n-140=0 equation:

Simplifying
6n2 + 2n + -140 = 0

Reorder the terms:
-140 + 2n + 6n2 = 0

Solving
-140 + 2n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-70 + n + 3n2) = 0

Factor a trinomial.
2((-5 + -1n)(14 + -3n)) = 0

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

Simplifying
-5 + -1n = 0

Solving
-5 + -1n = 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 + -1n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1n = 0 + 5
-1n = 0 + 5

Combine like terms: 0 + 5 = 5
-1n = 5

Divide each side by '-1'.
n = -5

Simplifying
n = -5
Subproblem 2
Set the factor '(14 + -3n)' equal to zero and attempt to solve:

Simplifying
14 + -3n = 0

Solving
14 + -3n = 0

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

Add '-14' to each side of the equation.
14 + -14 + -3n = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -3n = 0 + -14
-3n = 0 + -14

Combine like terms: 0 + -14 = -14
-3n = -14

Divide each side by '-3'.
n = 4.666666667

Simplifying
n = 4.666666667
Solution
n = {-5, 4.666666667}