(5n+1)(3n-2)=0

Solution for (5n+1)(3n-2)=0 equation:

Simplifying
(5n + 1)(3n + -2) = 0

Reorder the terms:
(1 + 5n)(3n + -2) = 0

Reorder the terms:
(1 + 5n)(-2 + 3n) = 0

Multiply (1 + 5n) * (-2 + 3n)
(1(-2 + 3n) + 5n * (-2 + 3n)) = 0
((-2 * 1 + 3n * 1) + 5n * (-2 + 3n)) = 0
((-2 + 3n) + 5n * (-2 + 3n)) = 0
(-2 + 3n + (-2 * 5n + 3n * 5n)) = 0
(-2 + 3n + (-10n + 15n2)) = 0

Combine like terms: 3n + -10n = -7n
(-2 + -7n + 15n2) = 0

Solving
-2 + -7n + 15n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -5n)(2 + -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 '(2 + -3n)' equal to zero and attempt to solve:

Simplifying
2 + -3n = 0

Solving
2 + -3n = 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 + -3n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3n = 0 + -2
-3n = 0 + -2

Combine like terms: 0 + -2 = -2
-3n = -2

Divide each side by '-3'.
n = 0.6666666667

Simplifying
n = 0.6666666667
Solution
n = {-0.2, 0.6666666667}