a) To solve the equation 2x(x-1)=0, we can set each factor equal to zero and solve for x:

2x = 0 or x-1 = 0

For 2x = 0, divide both sides by 2 to get x = 0.

For x-1 = 0, add 1 to both sides to get x = 1.

Therefore, the solutions to the equation are x = 0 and x = 1.

b) To solve the equation (2x-4)(9-3x)=0, we can set each factor equal to zero and solve for x:

2x-4 = 0 or 9-3x = 0

For 2x-4 = 0, add 4 to both sides and divide by 2 to get x = 2.

For 9-3x = 0, subtract 9 from both sides and divide by -3 to get x = 3.

Therefore, the solutions to the equation are x = 2 and x = 3.

c) To solve the equation (x-1954)5=50, divide both sides by 5 to get:

x-1954 = 10

Add 1954 to both sides to get:

x = 1964

Therefore, the solution to the equation is x = 1964.

d) To solve the equation 30(60-x)=30, divide both sides by 30 to get:

60-x = 1

Subtract 60 from both sides to get:

-x = -59

Multiply both sides by -1 to get:

x = 59

Therefore, the solution to the equation is x = 59.