(4n-1)(n+2)=20n-5

Solution for (4n-1)(n+2)=20n-5 equation:

Simplifying
(4n + -1)(n + 2) = 20n + -5

Reorder the terms:
(-1 + 4n)(n + 2) = 20n + -5

Reorder the terms:
(-1 + 4n)(2 + n) = 20n + -5

Multiply (-1 + 4n) * (2 + n)
(-1(2 + n) + 4n * (2 + n)) = 20n + -5
((2 * -1 + n * -1) + 4n * (2 + n)) = 20n + -5
((-2 + -1n) + 4n * (2 + n)) = 20n + -5
(-2 + -1n + (2 * 4n + n * 4n)) = 20n + -5
(-2 + -1n + (8n + 4n2)) = 20n + -5

Combine like terms: -1n + 8n = 7n
(-2 + 7n + 4n2) = 20n + -5

Reorder the terms:
-2 + 7n + 4n2 = -5 + 20n

Solving
-2 + 7n + 4n2 = -5 + 20n

Solving for variable 'n'.

Reorder the terms:
-2 + 5 + 7n + -20n + 4n2 = -5 + 20n + 5 + -20n

Combine like terms: -2 + 5 = 3
3 + 7n + -20n + 4n2 = -5 + 20n + 5 + -20n

Combine like terms: 7n + -20n = -13n
3 + -13n + 4n2 = -5 + 20n + 5 + -20n

Reorder the terms:
3 + -13n + 4n2 = -5 + 5 + 20n + -20n

Combine like terms: -5 + 5 = 0
3 + -13n + 4n2 = 0 + 20n + -20n
3 + -13n + 4n2 = 20n + -20n

Combine like terms: 20n + -20n = 0
3 + -13n + 4n2 = 0

Factor a trinomial.
(1 + -4n)(3 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.25, 3}