(7n-6)(7n+5)=

Solution for (7n-6)(7n+5)= equation:

Simplifying
(7n + -6)(7n + 5) = 0

Reorder the terms:
(-6 + 7n)(7n + 5) = 0

Reorder the terms:
(-6 + 7n)(5 + 7n) = 0

Multiply (-6 + 7n) * (5 + 7n)
(-6(5 + 7n) + 7n * (5 + 7n)) = 0
((5 * -6 + 7n * -6) + 7n * (5 + 7n)) = 0
((-30 + -42n) + 7n * (5 + 7n)) = 0
(-30 + -42n + (5 * 7n + 7n * 7n)) = 0
(-30 + -42n + (35n + 49n2)) = 0

Combine like terms: -42n + 35n = -7n
(-30 + -7n + 49n2) = 0

Solving
-30 + -7n + 49n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(-5 + -7n)(6 + -7n) = 0

Subproblem 1
Set the factor '(-5 + -7n)' equal to zero and attempt to solve:

Simplifying
-5 + -7n = 0

Solving
-5 + -7n = 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 + -7n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7n = 0 + 5
-7n = 0 + 5

Combine like terms: 0 + 5 = 5
-7n = 5

Divide each side by '-7'.
n = -0.7142857143

Simplifying
n = -0.7142857143
Subproblem 2
Set the factor '(6 + -7n)' equal to zero and attempt to solve:

Simplifying
6 + -7n = 0

Solving
6 + -7n = 0

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

Add '-6' to each side of the equation.
6 + -6 + -7n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -7n = 0 + -6
-7n = 0 + -6

Combine like terms: 0 + -6 = -6
-7n = -6

Divide each side by '-7'.
n = 0.8571428571

Simplifying
n = 0.8571428571
Solution
n = {-0.7142857143, 0.8571428571}