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5\left(z+4\right)-4\left(z-17\right)=60
Multiply both sides of the equation by 20, the least common multiple of 4,5.
5z+20-4\left(z-17\right)=60
Use the distributive property to multiply 5 by z+4.
5z+20-4z+68=60
Use the distributive property to multiply -4 by z-17.
z+20+68=60
Combine 5z and -4z to get z.
z+88=60
Add 20 and 68 to get 88.
z=60-88
Subtract 88 from both sides.
z=-28
Subtract 88 from 60 to get -28.