Final answer:
To solve the equation 12x³-3x²=0, factor out the GCF, set each factor equal to zero, and solve for x, resulting in two solutions: x=0 and x=1/4.
Step-by-step explanation:
To solve the equation 12x³-3x²=0 by factoring, we first identify the greatest common factor (GCF) of the terms, which is 3x². Factoring this out, we get 3x²(4x-1)=0.
Next, we set each factor equal to zero: 3x² = 0 and 4x - 1 = 0. From the first equation, we can immediately see that one solution for x is 0. For the second factor, we add 1 to both sides, getting 4x = 1, then divide both sides by 4 to find that x = 1/4.
Therefore, the solutions for the equation are x = 0 and x = 1/4.