4n^2+20n-73=2

Solution for 4n^2+20n-73=2 equation:

Simplifying
4n2 + 20n + -73 = 2

Reorder the terms:
-73 + 20n + 4n2 = 2

Solving
-73 + 20n + 4n2 = 2

Solving for variable 'n'.

Reorder the terms:
-73 + -2 + 20n + 4n2 = 2 + -2

Combine like terms: -73 + -2 = -75
-75 + 20n + 4n2 = 2 + -2

Combine like terms: 2 + -2 = 0
-75 + 20n + 4n2 = 0

Factor a trinomial.
(-15 + -2n)(5 + -2n) = 0

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

Simplifying
-15 + -2n = 0

Solving
-15 + -2n = 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 + -2n = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2n = 0 + 15
-2n = 0 + 15

Combine like terms: 0 + 15 = 15
-2n = 15

Divide each side by '-2'.
n = -7.5

Simplifying
n = -7.5
Subproblem 2
Set the factor '(5 + -2n)' equal to zero and attempt to solve:

Simplifying
5 + -2n = 0

Solving
5 + -2n = 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 + -2n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2n = 0 + -5
-2n = 0 + -5

Combine like terms: 0 + -5 = -5
-2n = -5

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {-7.5, 2.5}