(7n-2)(5n-15)=0

Solution for (7n-2)(5n-15)=0 equation:

Simplifying
(7n + -2)(5n + -15) = 0

Reorder the terms:
(-2 + 7n)(5n + -15) = 0

Reorder the terms:
(-2 + 7n)(-15 + 5n) = 0

Multiply (-2 + 7n) * (-15 + 5n)
(-2(-15 + 5n) + 7n * (-15 + 5n)) = 0
((-15 * -2 + 5n * -2) + 7n * (-15 + 5n)) = 0
((30 + -10n) + 7n * (-15 + 5n)) = 0
(30 + -10n + (-15 * 7n + 5n * 7n)) = 0
(30 + -10n + (-105n + 35n2)) = 0

Combine like terms: -10n + -105n = -115n
(30 + -115n + 35n2) = 0

Solving
30 + -115n + 35n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -23n + 7n2) = 0

Factor a trinomial.
5((2 + -7n)(3 + -1n)) = 0

Ignore the factor 5.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 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 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Solution
n = {0.2857142857, 3}