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

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

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

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

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

Multiply (5 + 2n) * (-1 + 7n)
(5(-1 + 7n) + 2n * (-1 + 7n)) = 0
((-1 * 5 + 7n * 5) + 2n * (-1 + 7n)) = 0
((-5 + 35n) + 2n * (-1 + 7n)) = 0
(-5 + 35n + (-1 * 2n + 7n * 2n)) = 0
(-5 + 35n + (-2n + 14n2)) = 0

Combine like terms: 35n + -2n = 33n
(-5 + 33n + 14n2) = 0

Solving
-5 + 33n + 14n2 = 0

Solving for variable 'n'.

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

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

Simplifying
-5 + -2n = 0

Solving
-5 + -2n = 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 + -2n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2n = 0 + 5
-2n = 0 + 5

Combine like terms: 0 + 5 = 5
-2n = 5

Divide each side by '-2'.
n = -2.5

Simplifying
n = -2.5
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 = {-2.5, 0.1428571429}