(n-7)(n-2)=

Solution for (n-7)(n-2)= equation:

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

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

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

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

Combine like terms: -7n + -2n = -9n
(14 + -9n + n2) = 0

Solving
14 + -9n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1n = 0 + -7

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

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

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {2, 7}