=(n+2)(n-7)

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

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

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

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

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

Combine like terms: 2n + -7n = -5n
0 = (-14 + -5n + n2)

Solving
0 = -14 + -5n + n2

Solving for variable 'n'.

Combine like terms: 0 + 14 = 14
14 + 5n + -1n2 = -14 + -5n + n2 + 14 + 5n + -1n2

Reorder the terms:
14 + 5n + -1n2 = -14 + 14 + -5n + 5n + n2 + -1n2

Combine like terms: -14 + 14 = 0
14 + 5n + -1n2 = 0 + -5n + 5n + n2 + -1n2
14 + 5n + -1n2 = -5n + 5n + n2 + -1n2

Combine like terms: -5n + 5n = 0
14 + 5n + -1n2 = 0 + n2 + -1n2
14 + 5n + -1n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
14 + 5n + -1n2 = 0

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

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

Simplifying
2 + n = 0

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

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

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

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