3x(4yz-3)-(5xyz-6x)=0

Solution for 3x(4yz-3)-(5xyz-6x)=0 equation:

Simplifying
3x(4yz + -3) + -1(5xyz + -6x) = 0

Reorder the terms:
3x(-3 + 4yz) + -1(5xyz + -6x) = 0
(-3 * 3x + 4yz * 3x) + -1(5xyz + -6x) = 0
(-9x + 12xyz) + -1(5xyz + -6x) = 0

Reorder the terms:
-9x + 12xyz + -1(-6x + 5xyz) = 0
-9x + 12xyz + (-6x * -1 + 5xyz * -1) = 0
-9x + 12xyz + (6x + -5xyz) = 0

Reorder the terms:
-9x + 6x + 12xyz + -5xyz = 0

Combine like terms: -9x + 6x = -3x
-3x + 12xyz + -5xyz = 0

Combine like terms: 12xyz + -5xyz = 7xyz
-3x + 7xyz = 0

Solving
-3x + 7xyz = 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), 'x'.
x(-3 + 7yz) = 0

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 '(-3 + 7yz)' equal to zero and attempt to solve:

Simplifying
-3 + 7yz = 0

Solving
-3 + 7yz = 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 + 7yz = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 7yz = 0 + 3
7yz = 0 + 3

Combine like terms: 0 + 3 = 3
7yz = 3

Add '-7yz' to each side of the equation.
7yz + -7yz = 3 + -7yz

Combine like terms: 7yz + -7yz = 0
0 = 3 + -7yz

Simplifying
0 = 3 + -7yz

The solution to this equation could not be determined.

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