If two numbers multiply to 0, then one or both of the numbers must be zero.
This rule is known as the zero product property
If A*B = 0 then either A = 0 or B = 0 (or both are zero)
Using that idea we go from
(6x-1)*(5x+3) = 0
to
6x-1=0 or 5x+3 = 0
Solve each new equation for x
6x-1 = 0
6x = 1
x = 1/6 <<--- this is the one of the solutions
and
5x+3 = 0
5x = -3
x = -3/5 <<--- and this is another solution