3(x+4)(x+3)=0

Solution for 3(x+4)(x+3)=0 equation:

Simplifying
3(x + 4)(x + 3) = 0

Reorder the terms:
3(4 + x)(x + 3) = 0

Reorder the terms:
3(4 + x)(3 + x) = 0

Multiply (4 + x) * (3 + x)
3(4(3 + x) + x(3 + x)) = 0
3((3 * 4 + x * 4) + x(3 + x)) = 0
3((12 + 4x) + x(3 + x)) = 0
3(12 + 4x + (3 * x + x * x)) = 0
3(12 + 4x + (3x + x2)) = 0

Combine like terms: 4x + 3x = 7x
3(12 + 7x + x2) = 0
(12 * 3 + 7x * 3 + x2 * 3) = 0
(36 + 21x + 3x2) = 0

Solving
36 + 21x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 7x + x2) = 0

Factor a trinomial.
3((4 + x)(3 + x)) = 0

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

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4
Subproblem 2
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
Solution
x = {-4, -3}