20n^2+15n=5

Solution for 20n^2+15n=5 equation:

Simplifying
20n2 + 15n = 5

Reorder the terms:
15n + 20n2 = 5

Solving
15n + 20n2 = 5

Solving for variable 'n'.

Reorder the terms:
-5 + 15n + 20n2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 15n + 20n2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 3n + 4n2) = 0

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

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

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 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 + -1n = 0 + 1

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

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

Divide each side by '-1'.
n = -1

Simplifying
n = -1
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 = {-1, 0.25}