(X+5)(X+5+7)=0

Solution for (X+5)(X+5+7)=0 equation:

Simplifying
(X + 5)(X + 5 + 7) = 0

Reorder the terms:
(5 + X)(X + 5 + 7) = 0

Reorder the terms:
(5 + X)(5 + 7 + X) = 0

Combine like terms: 5 + 7 = 12
(5 + X)(12 + X) = 0

Multiply (5 + X) * (12 + X)
(5(12 + X) + X(12 + X)) = 0
((12 * 5 + X * 5) + X(12 + X)) = 0
((60 + 5X) + X(12 + X)) = 0
(60 + 5X + (12 * X + X * X)) = 0
(60 + 5X + (12X + X2)) = 0

Combine like terms: 5X + 12X = 17X
(60 + 17X + X2) = 0

Solving
60 + 17X + X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(12 + X)(5 + X) = 0

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

Simplifying
12 + X = 0

Solving
12 + X = 0

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

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

Combine like terms: 12 + -12 = 0
0 + X = 0 + -12
X = 0 + -12

Combine like terms: 0 + -12 = -12
X = -12

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

Simplifying
5 + X = 0

Solving
5 + X = 0

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

Add '-5' to each side of the equation.
5 + -5 + X = 0 + -5

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

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

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