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4\times 3z=5\left(2z+1\right)
Multiply both sides of the equation by 20, the least common multiple of 5,4.
12z=5\left(2z+1\right)
Multiply 4 and 3 to get 12.
12z=10z+5
Use the distributive property to multiply 5 by 2z+1.
12z-10z=5
Subtract 10z from both sides.
2z=5
Combine 12z and -10z to get 2z.
z=\frac{5}{2}
Divide both sides by 2.