(7n-6)(8n+6)=

Solution for (7n-6)(8n+6)= equation:

Simplifying
(7n + -6)(8n + 6) = 0

Reorder the terms:
(-6 + 7n)(8n + 6) = 0

Reorder the terms:
(-6 + 7n)(6 + 8n) = 0

Multiply (-6 + 7n) * (6 + 8n)
(-6(6 + 8n) + 7n * (6 + 8n)) = 0
((6 * -6 + 8n * -6) + 7n * (6 + 8n)) = 0
((-36 + -48n) + 7n * (6 + 8n)) = 0
(-36 + -48n + (6 * 7n + 8n * 7n)) = 0
(-36 + -48n + (42n + 56n2)) = 0

Combine like terms: -48n + 42n = -6n
(-36 + -6n + 56n2) = 0

Solving
-36 + -6n + 56n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-18 + -3n + 28n2) = 0

Factor a trinomial.
2((-3 + -4n)(6 + -7n)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4n)' equal to zero and attempt to solve:

Simplifying
-3 + -4n = 0

Solving
-3 + -4n = 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 + -4n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4n = 0 + 3
-4n = 0 + 3

Combine like terms: 0 + 3 = 3
-4n = 3

Divide each side by '-4'.
n = -0.75

Simplifying
n = -0.75
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 = {-0.75, 0.8571428571}