(n+3)(n+3-9)=70

Solution for (n+3)(n+3-9)=70 equation:

Simplifying
(n + 3)(n + 3 + -9) = 70

Reorder the terms:
(3 + n)(n + 3 + -9) = 70

Reorder the terms:
(3 + n)(3 + -9 + n) = 70

Combine like terms: 3 + -9 = -6
(3 + n)(-6 + n) = 70

Multiply (3 + n) * (-6 + n)
(3(-6 + n) + n(-6 + n)) = 70
((-6 * 3 + n * 3) + n(-6 + n)) = 70
((-18 + 3n) + n(-6 + n)) = 70
(-18 + 3n + (-6 * n + n * n)) = 70
(-18 + 3n + (-6n + n2)) = 70

Combine like terms: 3n + -6n = -3n
(-18 + -3n + n2) = 70

Solving
-18 + -3n + n2 = 70

Solving for variable 'n'.

Reorder the terms:
-18 + -70 + -3n + n2 = 70 + -70

Combine like terms: -18 + -70 = -88
-88 + -3n + n2 = 70 + -70

Combine like terms: 70 + -70 = 0
-88 + -3n + n2 = 0

Factor a trinomial.
(-8 + -1n)(11 + -1n) = 0

Subproblem 1
Set the factor '(-8 + -1n)' equal to zero and attempt to solve:

Simplifying
-8 + -1n = 0

Solving
-8 + -1n = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1n = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1n = 0 + 8
-1n = 0 + 8

Combine like terms: 0 + 8 = 8
-1n = 8

Divide each side by '-1'.
n = -8

Simplifying
n = -8
Subproblem 2
Set the factor '(11 + -1n)' equal to zero and attempt to solve:

Simplifying
11 + -1n = 0

Solving
11 + -1n = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1n = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1n = 0 + -11
-1n = 0 + -11

Combine like terms: 0 + -11 = -11
-1n = -11

Divide each side by '-1'.
n = 11

Simplifying
n = 11
Solution
n = {-8, 11}