1)
Factor out an x from the equation:

x(-2x + 13) = 0

Set each factor equal to zero:

x = 0 or -2x + 13 = 0

-2x = -13

x = 13/2

Therefore, the solutions to the equation -2x^2 + 13x = 0 are x = 0 and x = 13/2.

2)
Factor out a 2b from the equation:

2b(3b - 1) = 0

Set each factor equal to zero:

2b = 0 or 3b - 1 = 0

b = 0 or 3b = 1

b = 0 or b = 1/3

Therefore, the solutions to the equation 6b^2 - 2b = 0 are b = 0 and b = 1/3.