Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{32-v-8z}{2\left(z-4\right)}\text{, }&z\neq 4\\x\in \mathrm{C}\text{, }&v=0\text{ and }z=4\end{matrix}\right.
Solve for v
v=2\left(x-4\right)\left(z-4\right)
Solve for x
\left\{\begin{matrix}x=-\frac{32-v-8z}{2\left(z-4\right)}\text{, }&z\neq 4\\x\in \mathrm{R}\text{, }&v=0\text{ and }z=4\end{matrix}\right.
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\left(zx-4z-4x+16\right)\times 2=v
Use the distributive property to multiply z-4 by x-4.
2zx-8z-8x+32=v
Use the distributive property to multiply zx-4z-4x+16 by 2.
2zx-8x+32=v+8z
Add 8z to both sides.
2zx-8x=v+8z-32
Subtract 32 from both sides.
\left(2z-8\right)x=v+8z-32
Combine all terms containing x.
\left(2z-8\right)x=8z+v-32
The equation is in standard form.
\frac{\left(2z-8\right)x}{2z-8}=\frac{8z+v-32}{2z-8}
Divide both sides by 2z-8.
x=\frac{8z+v-32}{2z-8}
Dividing by 2z-8 undoes the multiplication by 2z-8.
x=\frac{8z+v-32}{2\left(z-4\right)}
Divide v+8z-32 by 2z-8.
\left(zx-4z-4x+16\right)\times 2=v
Use the distributive property to multiply z-4 by x-4.
2zx-8z-8x+32=v
Use the distributive property to multiply zx-4z-4x+16 by 2.
v=2zx-8z-8x+32
Swap sides so that all variable terms are on the left hand side.
\left(zx-4z-4x+16\right)\times 2=v
Use the distributive property to multiply z-4 by x-4.
2zx-8z-8x+32=v
Use the distributive property to multiply zx-4z-4x+16 by 2.
2zx-8x+32=v+8z
Add 8z to both sides.
2zx-8x=v+8z-32
Subtract 32 from both sides.
\left(2z-8\right)x=v+8z-32
Combine all terms containing x.
\left(2z-8\right)x=8z+v-32
The equation is in standard form.
\frac{\left(2z-8\right)x}{2z-8}=\frac{8z+v-32}{2z-8}
Divide both sides by 2z-8.
x=\frac{8z+v-32}{2z-8}
Dividing by 2z-8 undoes the multiplication by 2z-8.
x=\frac{8z+v-32}{2\left(z-4\right)}
Divide v+8z-32 by 2z-8.
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