a) $4 x^{2}+3 x=0$

Step 1 ：Factor out an x from the equation: \(x(4x + 3) = 0\)

Step 2 ：Solve for the two possible values of x: \(x = 0\) and \(4x + 3 = 0\)

Step 3 ：Solve for x in the second equation: \(x = -\frac{3}{4}\)

Step 4 ：\(\boxed{x = -\frac{3}{4}, x = 0}\)