12x^2y^2-27x^2z^2=0

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Solution for 12x^2y^2-27x^2z^2=0 equation: 


Simplifying
12x2y2 + -27x2z2 = 0

Solving
12x2y2 + -27x2z2 = 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), '3x2'.
3x2(4y2 + -9z2) = 0

Factor a difference between two squares.
3x2((2y + 3z)(2y + -3z)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(2y + 3z)' equal to zero and attempt to solve:

Simplifying
2y + 3z = 0

Solving
2y + 3z = 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 + 3z = 0 + -2y

Combine like terms: 2y + -2y = 0
0 + 3z = 0 + -2y
3z = 0 + -2y
Remove the zero:
3z = -2y

Add '-3z' to each side of the equation.
3z + -3z = -2y + -3z

Combine like terms: 3z + -3z = 0
0 = -2y + -3z

Simplifying
0 = -2y + -3z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(2y + -3z)' equal to zero and attempt to solve:

Simplifying
2y + -3z = 0

Solving
2y + -3z = 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 + -3z = 0 + -2y

Combine like terms: 2y + -2y = 0
0 + -3z = 0 + -2y
-3z = 0 + -2y
Remove the zero:
-3z = -2y

Add '3z' to each side of the equation.
-3z + 3z = -2y + 3z

Combine like terms: -3z + 3z = 0
0 = -2y + 3z

Simplifying
0 = -2y + 3z

The solution to this equation could not be determined.

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

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