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

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

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

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

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

Multiply (-5 + 3n) * (1 + 5n)
(-5(1 + 5n) + 3n * (1 + 5n)) = 0
((1 * -5 + 5n * -5) + 3n * (1 + 5n)) = 0
((-5 + -25n) + 3n * (1 + 5n)) = 0
(-5 + -25n + (1 * 3n + 5n * 3n)) = 0
(-5 + -25n + (3n + 15n2)) = 0

Combine like terms: -25n + 3n = -22n
(-5 + -22n + 15n2) = 0

Solving
-5 + -22n + 15n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -5n)(5 + -3n) = 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 '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {-0.2, 1.666666667}