(2n-1)(10n+3)=0

Solution for (2n-1)(10n+3)=0 equation:

Simplifying
(2n + -1)(10n + 3) = 0

Reorder the terms:
(-1 + 2n)(10n + 3) = 0

Reorder the terms:
(-1 + 2n)(3 + 10n) = 0

Multiply (-1 + 2n) * (3 + 10n)
(-1(3 + 10n) + 2n * (3 + 10n)) = 0
((3 * -1 + 10n * -1) + 2n * (3 + 10n)) = 0
((-3 + -10n) + 2n * (3 + 10n)) = 0
(-3 + -10n + (3 * 2n + 10n * 2n)) = 0
(-3 + -10n + (6n + 20n2)) = 0

Combine like terms: -10n + 6n = -4n
(-3 + -4n + 20n2) = 0

Solving
-3 + -4n + 20n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-3 + -10n)(1 + -2n) = 0

Subproblem 1
Set the factor '(-3 + -10n)' equal to zero and attempt to solve:

Simplifying
-3 + -10n = 0

Solving
-3 + -10n = 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 + -10n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -10n = 0 + 3
-10n = 0 + 3

Combine like terms: 0 + 3 = 3
-10n = 3

Divide each side by '-10'.
n = -0.3

Simplifying
n = -0.3
Subproblem 2
Set the factor '(1 + -2n)' equal to zero and attempt to solve:

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
Solution
n = {-0.3, 0.5}