(5n+1)(7n-1)=

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

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

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

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

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

Combine like terms: 7n + -5n = 2n
(-1 + 2n + 35n2) = 0

Solving
-1 + 2n + 35n2 = 0

Solving for variable 'n'.

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

Simplifying
1 + -7n = 0

Solving
1 + -7n = 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 + -7n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7n = 0 + -1
-7n = 0 + -1

Combine like terms: 0 + -1 = -1
-7n = -1

Divide each side by '-7'.
n = 0.1428571429

Simplifying
n = 0.1428571429
Solution
n = {-0.2, 0.1428571429}