2n^2+9n-23=3

Solution for 2n^2+9n-23=3 equation:

Simplifying
2n2 + 9n + -23 = 3

Reorder the terms:
-23 + 9n + 2n2 = 3

Solving
-23 + 9n + 2n2 = 3

Solving for variable 'n'.

Reorder the terms:
-23 + -3 + 9n + 2n2 = 3 + -3

Combine like terms: -23 + -3 = -26
-26 + 9n + 2n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-26 + 9n + 2n2 = 0

Factor a trinomial.
(-13 + -2n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -2n)' equal to zero and attempt to solve:

Simplifying
-13 + -2n = 0

Solving
-13 + -2n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -2n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -2n = 0 + 13
-2n = 0 + 13

Combine like terms: 0 + 13 = 13
-2n = 13

Divide each side by '-2'.
n = -6.5

Simplifying
n = -6.5
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-6.5, 2}