Solve this quadratic equation: (2x-1)(3x+5)=(x+2)(2x-1)

First, note that because this is a quadratic equation,
there must be two roots. You might be tempted to divide both sides by (2x-1), and get
rid of it; but this discards one of your roots.

(2x - 1) =
0    --> This must be true, because you're multiplying both sides by it.
Therefore, either it is zero, OR both 3x + 5 = 0 and x + 2 = 0, which is impossible.
Thus, x = 1/2 is your first root.

To get the second root,
divide by 2x-1 to get:

3x + 5 = x + 2  --> x = -3/2,
your second root

Alternatively, you could have
multiplied the two sides out and combined like terms to get the quadratic
formula:

6 x^2+7 x-5 = 2 x^2+3
x-2

4x^2 + 4x - 3 = 0

x = (b
+/- sqrt(b^2 - 4ac) ) /2a

yields x = 1/2,
-2/3