5n^2+44n+20=2n+4

Solution for 5n^2+44n+20=2n+4 equation:

Simplifying
5n2 + 44n + 20 = 2n + 4

Reorder the terms:
20 + 44n + 5n2 = 2n + 4

Reorder the terms:
20 + 44n + 5n2 = 4 + 2n

Solving
20 + 44n + 5n2 = 4 + 2n

Solving for variable 'n'.

Reorder the terms:
20 + -4 + 44n + -2n + 5n2 = 4 + 2n + -4 + -2n

Combine like terms: 20 + -4 = 16
16 + 44n + -2n + 5n2 = 4 + 2n + -4 + -2n

Combine like terms: 44n + -2n = 42n
16 + 42n + 5n2 = 4 + 2n + -4 + -2n

Reorder the terms:
16 + 42n + 5n2 = 4 + -4 + 2n + -2n

Combine like terms: 4 + -4 = 0
16 + 42n + 5n2 = 0 + 2n + -2n
16 + 42n + 5n2 = 2n + -2n

Combine like terms: 2n + -2n = 0
16 + 42n + 5n2 = 0

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

Subproblem 1
Set the factor '(8 + n)' equal to zero and attempt to solve:

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

Combine like terms: 8 + -8 = 0
0 + n = 0 + -8
n = 0 + -8

Combine like terms: 0 + -8 = -8
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

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

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

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

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {-8, -0.4}