5n^2-20n-20=-2+7n

Solution for 5n^2-20n-20=-2+7n equation:

Simplifying
5n2 + -20n + -20 = -2 + 7n

Reorder the terms:
-20 + -20n + 5n2 = -2 + 7n

Solving
-20 + -20n + 5n2 = -2 + 7n

Solving for variable 'n'.

Reorder the terms:
-20 + 2 + -20n + -7n + 5n2 = -2 + 7n + 2 + -7n

Combine like terms: -20 + 2 = -18
-18 + -20n + -7n + 5n2 = -2 + 7n + 2 + -7n

Combine like terms: -20n + -7n = -27n
-18 + -27n + 5n2 = -2 + 7n + 2 + -7n

Reorder the terms:
-18 + -27n + 5n2 = -2 + 2 + 7n + -7n

Combine like terms: -2 + 2 = 0
-18 + -27n + 5n2 = 0 + 7n + -7n
-18 + -27n + 5n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
-18 + -27n + 5n2 = 0

Factor a trinomial.
(-3 + -5n)(6 + -1n) = 0

Subproblem 1
Set the factor '(-3 + -5n)' equal to zero and attempt to solve:

Simplifying
-3 + -5n = 0

Solving
-3 + -5n = 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 + -5n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5n = 0 + 3
-5n = 0 + 3

Combine like terms: 0 + 3 = 3
-5n = 3

Divide each side by '-5'.
n = -0.6

Simplifying
n = -0.6
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 = {-0.6, 6}