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My answer is in the following picture, hopes it can help you ~
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Answer:

One solution.

Step-by-step explanation:

We have been given an equation [tex]20z-5-12z=10z+8[/tex]. We are asked to find the number of solutions for our given equation.

Let us solve our given equation. Upon combining like terms, we will get:

[tex]20z-12z-5=10z+8[/tex]

[tex]8z-5=10z+8[/tex]

[tex]8z-10z-5=10z-10z+8[/tex]

[tex]-2z-5=8[/tex]

[tex]-2z-5+5=8+5[/tex]

[tex]-2z=13[/tex]

[tex]\frac{-2z}{-2}=\frac{13}{-2}[/tex]

[tex]z=-\frac{13}{2}[/tex]

Therefore, our given equation has only one solution.