Solution:
5z2 =3z

z(5z)=(3)z

5z=3

z=3/5----(1)

5z2-3z=0

z(5z-3)=0

z=0/(5z-3)

z=0----(2)

from 1& 2 solutions are =0 & 3/5

Problem: Solve the equation 5z^2 = 3z.

Solution:

To solve the given equation, we need to find the value(s) of z that satisfy the equation. We can do this by rearranging the equation and solving for z.

Step 1: Rearrange the equation

To simplify the equation, we can move all terms to one side, so that the equation becomes quadratic in form.

5z^2 - 3z = 0

Step 2: Factor out common terms

Now, we can factor out z from the equation.

z(5z - 3) = 0

Step 3: Apply the zero product property

According to the zero product property, if the product of two factors is zero, then at least one of the factors must be zero.

Therefore, we set each factor equal to zero and solve for z.

z = 0 (Equation 1)

5z - 3 = 0 (Equation 2)

Step 4: Solve for z

Solving Equation 1, we find that z = 0.

Solving Equation 2, we can isolate z by adding 3 to both sides.

5z = 3

Dividing both sides by 5, we get:

z = 3/5.

Therefore, the solutions to the equation 5z^2 = 3z are z = 0 and z = 3/5.

Conclusion:

The correct answer is option 'A', which states that the solutions to the equation 5z^2 = 3z are z = 0 and z = 3/5.