(n-3)(n+9)=-35

Solution for (n-3)(n+9)=-35 equation:

Simplifying
(n + -3)(n + 9) = -35

Reorder the terms:
(-3 + n)(n + 9) = -35

Reorder the terms:
(-3 + n)(9 + n) = -35

Multiply (-3 + n) * (9 + n)
(-3(9 + n) + n(9 + n)) = -35
((9 * -3 + n * -3) + n(9 + n)) = -35
((-27 + -3n) + n(9 + n)) = -35
(-27 + -3n + (9 * n + n * n)) = -35
(-27 + -3n + (9n + n2)) = -35

Combine like terms: -3n + 9n = 6n
(-27 + 6n + n2) = -35

Solving
-27 + 6n + n2 = -35

Solving for variable 'n'.

Reorder the terms:
-27 + 35 + 6n + n2 = -35 + 35

Combine like terms: -27 + 35 = 8
8 + 6n + n2 = -35 + 35

Combine like terms: -35 + 35 = 0
8 + 6n + n2 = 0

Factor a trinomial.
(4 + n)(2 + n) = 0

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
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 = {-4, -2}