4n-20=n^2+2n-35

Solution for 4n-20=n^2+2n-35 equation:

Simplifying
4n + -20 = n2 + 2n + -35

Reorder the terms:
-20 + 4n = n2 + 2n + -35

Reorder the terms:
-20 + 4n = -35 + 2n + n2

Solving
-20 + 4n = -35 + 2n + n2

Solving for variable 'n'.

Reorder the terms:
-20 + 35 + 4n + -2n + -1n2 = -35 + 2n + n2 + 35 + -2n + -1n2

Combine like terms: -20 + 35 = 15
15 + 4n + -2n + -1n2 = -35 + 2n + n2 + 35 + -2n + -1n2

Combine like terms: 4n + -2n = 2n
15 + 2n + -1n2 = -35 + 2n + n2 + 35 + -2n + -1n2

Reorder the terms:
15 + 2n + -1n2 = -35 + 35 + 2n + -2n + n2 + -1n2

Combine like terms: -35 + 35 = 0
15 + 2n + -1n2 = 0 + 2n + -2n + n2 + -1n2
15 + 2n + -1n2 = 2n + -2n + n2 + -1n2

Combine like terms: 2n + -2n = 0
15 + 2n + -1n2 = 0 + n2 + -1n2
15 + 2n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
15 + 2n + -1n2 = 0

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

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 '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

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

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

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

Simplifying
n = -3
Solution
n = {5, -3}