=(n-2)(n-5)

Solution for =(n-2)(n-5) equation:

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

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

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

Multiply (-2 + n) * (-5 + n)
0 = (-2(-5 + n) + n(-5 + n))
0 = ((-5 * -2 + n * -2) + n(-5 + n))
0 = ((10 + -2n) + n(-5 + n))
0 = (10 + -2n + (-5 * n + n * n))
0 = (10 + -2n + (-5n + n2))

Combine like terms: -2n + -5n = -7n
0 = (10 + -7n + n2)

Solving
0 = 10 + -7n + n2

Solving for variable 'n'.

Combine like terms: 0 + -10 = -10
-10 + 7n + -1n2 = 10 + -7n + n2 + -10 + 7n + -1n2

Reorder the terms:
-10 + 7n + -1n2 = 10 + -10 + -7n + 7n + n2 + -1n2

Combine like terms: 10 + -10 = 0
-10 + 7n + -1n2 = 0 + -7n + 7n + n2 + -1n2
-10 + 7n + -1n2 = -7n + 7n + n2 + -1n2

Combine like terms: -7n + 7n = 0
-10 + 7n + -1n2 = 0 + n2 + -1n2
-10 + 7n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
-10 + 7n + -1n2 = 0

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

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

Simplifying
-5 + n = 0

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

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

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

Simplifying
n = 5
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 = {5, 2}