(7n-2)(3n-5)=

Solution for (7n-2)(3n-5)= equation:

Simplifying
(7n + -2)(3n + -5) = 0

Reorder the terms:
(-2 + 7n)(3n + -5) = 0

Reorder the terms:
(-2 + 7n)(-5 + 3n) = 0

Multiply (-2 + 7n) * (-5 + 3n)
(-2(-5 + 3n) + 7n * (-5 + 3n)) = 0
((-5 * -2 + 3n * -2) + 7n * (-5 + 3n)) = 0
((10 + -6n) + 7n * (-5 + 3n)) = 0
(10 + -6n + (-5 * 7n + 3n * 7n)) = 0
(10 + -6n + (-35n + 21n2)) = 0

Combine like terms: -6n + -35n = -41n
(10 + -41n + 21n2) = 0

Solving
10 + -41n + 21n2 = 0

Solving for variable 'n'.

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

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 '(5 + -3n)' equal to zero and attempt to solve:

Simplifying
5 + -3n = 0

Solving
5 + -3n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3n = 0 + -5
-3n = 0 + -5

Combine like terms: 0 + -5 = -5
-3n = -5

Divide each side by '-3'.
n = 1.666666667

Simplifying
n = 1.666666667
Solution
n = {0.2857142857, 1.666666667}