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left parenthesis, x, plus, y, right parenthesis, times, z, equals, z, x, plus, y, x
Solve for x
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Solve for y
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xz+yz=zx+yx
Use the distributive property to multiply x+y by z.
xz+yz-zx=yx
Subtract zx from both sides.
yz=yx
Combine xz and -zx to get 0.
yx=yz
Swap sides so that all variable terms are on the left hand side.
\frac{yx}{y}=\frac{yz}{y}
Divide both sides by y.
x=\frac{yz}{y}
Dividing by y undoes the multiplication by y.
x=z
Divide yz by y.
xz+yz=zx+yx
Use the distributive property to multiply x+y by z.
xz+yz-yx=zx
Subtract yx from both sides.
yz-yx=zx-xz
Subtract xz from both sides.
yz-yx=0
Combine zx and -xz to get 0.
\left(z-x\right)y=0
Combine all terms containing y.
y=0
Divide 0 by -x+z.