(4X+12)(X+1)=

Solution for (4X+12)(X+1)= equation:

Simplifying
(4X + 12)(X + 1) = 0

Reorder the terms:
(12 + 4X)(X + 1) = 0

Reorder the terms:
(12 + 4X)(1 + X) = 0

Multiply (12 + 4X) * (1 + X)
(12(1 + X) + 4X * (1 + X)) = 0
((1 * 12 + X * 12) + 4X * (1 + X)) = 0
((12 + 12X) + 4X * (1 + X)) = 0
(12 + 12X + (1 * 4X + X * 4X)) = 0
(12 + 12X + (4X + 4X2)) = 0

Combine like terms: 12X + 4X = 16X
(12 + 16X + 4X2) = 0

Solving
12 + 16X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3 + 4X + X2) = 0

Factor a trinomial.
4((3 + X)(1 + X)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(3 + X)' equal to zero and attempt to solve:

Simplifying
3 + X = 0

Solving
3 + X = 0

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

Add '-3' to each side of the equation.
3 + -3 + X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + X = 0 + -3
X = 0 + -3

Combine like terms: 0 + -3 = -3
X = -3

Simplifying
X = -3
Subproblem 2
Set the factor '(1 + X)' equal to zero and attempt to solve:

Simplifying
1 + X = 0

Solving
1 + X = 0

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

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

Combine like terms: 1 + -1 = 0
0 + X = 0 + -1
X = 0 + -1

Combine like terms: 0 + -1 = -1
X = -1

Simplifying
X = -1
Solution
X = {-3, -1}