(5n+1)(4n-3)=

Solution for (5n+1)(4n-3)= equation:

Simplifying
(5n + 1)(4n + -3) = 0

Reorder the terms:
(1 + 5n)(4n + -3) = 0

Reorder the terms:
(1 + 5n)(-3 + 4n) = 0

Multiply (1 + 5n) * (-3 + 4n)
(1(-3 + 4n) + 5n * (-3 + 4n)) = 0
((-3 * 1 + 4n * 1) + 5n * (-3 + 4n)) = 0
((-3 + 4n) + 5n * (-3 + 4n)) = 0
(-3 + 4n + (-3 * 5n + 4n * 5n)) = 0
(-3 + 4n + (-15n + 20n2)) = 0

Combine like terms: 4n + -15n = -11n
(-3 + -11n + 20n2) = 0

Solving
-3 + -11n + 20n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -5n)(3 + -4n) = 0

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

Simplifying
-1 + -5n = 0

Solving
-1 + -5n = 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 + -5n = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5n = 0 + 1
-5n = 0 + 1

Combine like terms: 0 + 1 = 1
-5n = 1

Divide each side by '-5'.
n = -0.2

Simplifying
n = -0.2
Subproblem 2
Set the factor '(3 + -4n)' equal to zero and attempt to solve:

Simplifying
3 + -4n = 0

Solving
3 + -4n = 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 + -4n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4n = 0 + -3
-4n = 0 + -3

Combine like terms: 0 + -3 = -3
-4n = -3

Divide each side by '-4'.
n = 0.75

Simplifying
n = 0.75
Solution
n = {-0.2, 0.75}