20n(n+1)=7n-2

Solution for 20n(n+1)=7n-2 equation:

Simplifying
20n(n + 1) = 7n + -2

Reorder the terms:
20n(1 + n) = 7n + -2
(1 * 20n + n * 20n) = 7n + -2
(20n + 20n2) = 7n + -2

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

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

Solving for variable 'n'.

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

Combine like terms: 20n + -7n = 13n
2 + 13n + 20n2 = -2 + 7n + 2 + -7n

Reorder the terms:
2 + 13n + 20n2 = -2 + 2 + 7n + -7n

Combine like terms: -2 + 2 = 0
2 + 13n + 20n2 = 0 + 7n + -7n
2 + 13n + 20n2 = 7n + -7n

Combine like terms: 7n + -7n = 0
2 + 13n + 20n2 = 0

Factor a trinomial.
(2 + 5n)(1 + 4n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(1 + 4n)' equal to zero and attempt to solve:

Simplifying
1 + 4n = 0

Solving
1 + 4n = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4n = 0 + -1
4n = 0 + -1

Combine like terms: 0 + -1 = -1
4n = -1

Divide each side by '4'.
n = -0.25

Simplifying
n = -0.25
Solution
n = {-0.4, -0.25}