(7n+7)(3n-6)=

Solution for (7n+7)(3n-6)= equation:

Simplifying
(7n + 7)(3n + -6) = 0

Reorder the terms:
(7 + 7n)(3n + -6) = 0

Reorder the terms:
(7 + 7n)(-6 + 3n) = 0

Multiply (7 + 7n) * (-6 + 3n)
(7(-6 + 3n) + 7n * (-6 + 3n)) = 0
((-6 * 7 + 3n * 7) + 7n * (-6 + 3n)) = 0
((-42 + 21n) + 7n * (-6 + 3n)) = 0
(-42 + 21n + (-6 * 7n + 3n * 7n)) = 0
(-42 + 21n + (-42n + 21n2)) = 0

Combine like terms: 21n + -42n = -21n
(-42 + -21n + 21n2) = 0

Solving
-42 + -21n + 21n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '21'.
21(-2 + -1n + n2) = 0

Factor a trinomial.
21((-1 + -1n)(2 + -1n)) = 0

Ignore the factor 21.
Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve:

Simplifying
-1 + -1n = 0

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

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

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

Divide each side by '-1'.
n = -1

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

Simplifying
2 + -1n = 0

Solving
2 + -1n = 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 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-1, 2}