Tewtor.ai

Dividing by 2 is just a convenience step—it makes the numbers smaller and the factoring easier, but it doesn’t change the solutions.

Why it works

The original equation is

Every term on the left side has a factor of 2. If we divide both sides of the equation by the same non‑zero number, the equality remains true:

Since $0/2 = 0$, we get

Because we performed the same operation on every term, any value of $x$ that satisfies the simplified equation will also satisfy the original one, and vice‑versa. In other words, the two equations are equivalent.

When you might skip this step

You could solve the original quadratic directly with the quadratic formula:

where $a = 2$, $b = -8$, and $c = 6$. That gives the same roots $x = 1$ and $x = 3$, but the arithmetic involves larger numbers (e.g., $b^{2}=64$ and $4ac=48$).

So dividing by the greatest common factor first is just a shortcut that reduces the arithmetic workload and makes factoring more obvious. The solutions are unchanged.