xy^2-xz^2=0

Solution for xy^2-xz^2=0 equation:

Simplifying
xy2 + -1xz2 = 0

Solving
xy2 + -1xz2 = 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(y2 + -1z2) = 0

Factor a difference between two squares.
x((y + z)(y + -1z)) = 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 '(y + z)' equal to zero and attempt to solve:

Simplifying
y + z = 0

Solving
y + z = 0

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

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

Combine like terms: y + -1y = 0
0 + z = 0 + -1y
z = 0 + -1y
Remove the zero:
z = -1y

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

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

Simplifying
0 = -1y + -1z

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 '(y + -1z)' equal to zero and attempt to solve:

Simplifying
y + -1z = 0

Solving
y + -1z = 0

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

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

Combine like terms: y + -1y = 0
0 + -1z = 0 + -1y
-1z = 0 + -1y
Remove the zero:
-1z = -1y

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

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

Simplifying
0 = -1y + z

The solution to this equation could not be determined.

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