n^2+2n-3=192

Solution for n^2+2n-3=192 equation:

Simplifying
n2 + 2n + -3 = 192

Reorder the terms:
-3 + 2n + n2 = 192

Solving
-3 + 2n + n2 = 192

Solving for variable 'n'.

Reorder the terms:
-3 + -192 + 2n + n2 = 192 + -192

Combine like terms: -3 + -192 = -195
-195 + 2n + n2 = 192 + -192

Combine like terms: 192 + -192 = 0
-195 + 2n + n2 = 0

Factor a trinomial.
(-15 + -1n)(13 + -1n) = 0

Subproblem 1
Set the factor '(-15 + -1n)' equal to zero and attempt to solve:

Simplifying
-15 + -1n = 0

Solving
-15 + -1n = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1n = 0 + 15
-1n = 0 + 15

Combine like terms: 0 + 15 = 15
-1n = 15

Divide each side by '-1'.
n = -15

Simplifying
n = -15
Subproblem 2
Set the factor '(13 + -1n)' equal to zero and attempt to solve:

Simplifying
13 + -1n = 0

Solving
13 + -1n = 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 + -1n = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1n = 0 + -13
-1n = 0 + -13

Combine like terms: 0 + -13 = -13
-1n = -13

Divide each side by '-1'.
n = 13

Simplifying
n = 13
Solution
n = {-15, 13}