(7n-2)(5n-1)=0

Solution for (7n-2)(5n-1)=0 equation:

Simplifying
(7n + -2)(5n + -1) = 0

Reorder the terms:
(-2 + 7n)(5n + -1) = 0

Reorder the terms:
(-2 + 7n)(-1 + 5n) = 0

Multiply (-2 + 7n) * (-1 + 5n)
(-2(-1 + 5n) + 7n * (-1 + 5n)) = 0
((-1 * -2 + 5n * -2) + 7n * (-1 + 5n)) = 0
((2 + -10n) + 7n * (-1 + 5n)) = 0
(2 + -10n + (-1 * 7n + 5n * 7n)) = 0
(2 + -10n + (-7n + 35n2)) = 0

Combine like terms: -10n + -7n = -17n
(2 + -17n + 35n2) = 0

Solving
2 + -17n + 35n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(1 + -5n)(2 + -7n) = 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 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

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

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Solution
n = {0.2, 0.2857142857}