3x(4y+2z)=

Solution for 3x(4y+2z)= equation:

Simplifying
3x(4y + 2z) = 0
(4y * 3x + 2z * 3x) = 0
(12xy + 6xz) = 0

Solving
12xy + 6xz = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '6x'.
6x(2y + z) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2y + z)' equal to zero and attempt to solve:

Simplifying
2y + z = 0

Solving
2y + z = 0

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

Add '-2y' to each side of the equation.
2y + -2y + z = 0 + -2y

Combine like terms: 2y + -2y = 0
0 + z = 0 + -2y
z = 0 + -2y
Remove the zero:
z = -2y

Add '-1z' to each side of the equation.
z + -1z = -2y + -1z

Combine like terms: z + -1z = 0
0 = -2y + -1z

Simplifying
0 = -2y + -1z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}