3x^2 + 2x = 0

Solve 3x^2 + 2x = 0.

• Factor: x(3x + 2) = 0
• Zero product property: x = 0 or 3x + 2 = 0

So the solutions are:

• x = 0
• x = -2/3

Alternative using the quadratic formula (a=3, b=2, c=0): x = [-2 ± sqrt(4)] / (2*3) = [-2 ± 2] / 6 → x = 0 or x = -2/3.