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Dividing the whole equation by 2 (the greatest common factor) is a useful first step because:

1. It simplifies the numbers – the coefficients become smaller, so the arithmetic in later steps is easier and less error‑prone.
2. It does not change the solutions – multiplying or dividing an equation by a non‑zero constant leaves the set of $x$ values that satisfy the equation unchanged. In other words, if $2x^{2}-8x+6=0$, then any $x$ that makes this true will also make $\frac{1}{2}(2x^{2}-8x+6)=0$, i.e. $x^{2}-4x+3=0$, and vice‑versa.
3. It prepares the quadratic for factoring – with smaller coefficients it’s easier to spot the pair of numbers that multiply to the constant term and add to the linear coefficient (here, –1 and –3).

Common mistake: dividing only one term (or only the first two terms) by the GCF changes the equation’s balance and leads to an incorrect solution. Always divide every term, including the constant term, by the same factor.

Try it yourself
Use the interactive “Quadratic Explorer” below to see how changing the coefficients affects the graph and the roots. You can also toggle the “Divide by GCF” button to watch the simplification step in action.