2n^2+9n-126=0

Solution for 2n^2+9n-126=0 equation:

Simplifying
2n2 + 9n + -126 = 0

Reorder the terms:
-126 + 9n + 2n2 = 0

Solving
-126 + 9n + 2n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-21 + -2n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-21 + -2n)' equal to zero and attempt to solve:

Simplifying
-21 + -2n = 0

Solving
-21 + -2n = 0

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

Add '21' to each side of the equation.
-21 + 21 + -2n = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -2n = 0 + 21
-2n = 0 + 21

Combine like terms: 0 + 21 = 21
-2n = 21

Divide each side by '-2'.
n = -10.5

Simplifying
n = -10.5
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 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 + -1n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1n = 0 + -6
-1n = 0 + -6

Combine like terms: 0 + -6 = -6
-1n = -6

Divide each side by '-1'.
n = 6

Simplifying
n = 6
Solution
n = {-10.5, 6}