(n+2)(n+5)=70

Solution for (n+2)(n+5)=70 equation:

Simplifying
(n + 2)(n + 5) = 70

Reorder the terms:
(2 + n)(n + 5) = 70

Reorder the terms:
(2 + n)(5 + n) = 70

Multiply (2 + n) * (5 + n)
(2(5 + n) + n(5 + n)) = 70
((5 * 2 + n * 2) + n(5 + n)) = 70
((10 + 2n) + n(5 + n)) = 70
(10 + 2n + (5 * n + n * n)) = 70
(10 + 2n + (5n + n2)) = 70

Combine like terms: 2n + 5n = 7n
(10 + 7n + n2) = 70

Solving
10 + 7n + n2 = 70

Solving for variable 'n'.

Reorder the terms:
10 + -70 + 7n + n2 = 70 + -70

Combine like terms: 10 + -70 = -60
-60 + 7n + n2 = 70 + -70

Combine like terms: 70 + -70 = 0
-60 + 7n + n2 = 0

Factor a trinomial.
(-12 + -1n)(5 + -1n) = 0

Subproblem 1
Set the factor '(-12 + -1n)' equal to zero and attempt to solve:

Simplifying
-12 + -1n = 0

Solving
-12 + -1n = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1n = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1n = 0 + 12
-1n = 0 + 12

Combine like terms: 0 + 12 = 12
-1n = 12

Divide each side by '-1'.
n = -12

Simplifying
n = -12
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

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

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

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {-12, 5}