Tewtor.ai

Dividing the whole equation by 2 is just a simplifying step.

• The original equation is

  $$2x^{2}-8x+6=0$$

• Every term (the left‑hand side) has a common factor of 2.

• If we divide both sides of the equation by the same non‑zero number, the equality stays true. In other words,

  $$\frac{2x^{2}}{2}-\frac{8x}{2}+\frac{6}{2}= \frac{0}{2}$$

  which reduces to

  $$x^{2}-4x+3=0$$

Why do this?

1. Easier arithmetic – smaller numbers make factoring or using the quadratic formula less error‑prone.
2. Same solutions – dividing by a non‑zero constant does not change the roots; any $x$ that satisfies the simplified equation also satisfies the original one, and vice‑versa.

You could solve the original equation without dividing, but you’d have to factor a quadratic with a leading coefficient of 2, which is a bit messier. After simplifying, the quadratic factors cleanly as $(x-1)(x-3)=0$, giving the solutions $x=1$ and $x=3$.

Let me know if you’d like to see the alternative method (using the quadratic formula on the original form) or any other part clarified!