(7n-3)(2n+1)=0

Solution for (7n-3)(2n+1)=0 equation:

Simplifying
(7n + -3)(2n + 1) = 0

Reorder the terms:
(-3 + 7n)(2n + 1) = 0

Reorder the terms:
(-3 + 7n)(1 + 2n) = 0

Multiply (-3 + 7n) * (1 + 2n)
(-3(1 + 2n) + 7n * (1 + 2n)) = 0
((1 * -3 + 2n * -3) + 7n * (1 + 2n)) = 0
((-3 + -6n) + 7n * (1 + 2n)) = 0
(-3 + -6n + (1 * 7n + 2n * 7n)) = 0
(-3 + -6n + (7n + 14n2)) = 0

Combine like terms: -6n + 7n = 1n
(-3 + 1n + 14n2) = 0

Solving
-3 + 1n + 14n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-1 + -2n)(3 + -7n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -7n)' equal to zero and attempt to solve:

Simplifying
3 + -7n = 0

Solving
3 + -7n = 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 + -7n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -7n = 0 + -3
-7n = 0 + -3

Combine like terms: 0 + -3 = -3
-7n = -3

Divide each side by '-7'.
n = 0.4285714286

Simplifying
n = 0.4285714286
Solution
n = {-0.5, 0.4285714286}