Arrange It First

The zero product rule needs a zero on one side. $x^{2} = 7x-10$ has no zero, so make one. Move every term to the left side: $x^{2}-7x+10 = 0$. Now factor and set each factor equal to zero: $\left(x-2\right)\left(x-5\right) = 0$, so $x = 2$ or $x = 5$.

Do not skip this step. From $\left(x-1\right)\left(x+2\right) = 4$ you cannot conclude that one factor is 4. Many products equal 4 without either factor being 4, for example $2\cdot 2$. The rule works only for a product that equals zero.

The full method has three steps. First, move every term to one side so that the other side is 0. Second, factor. Third, set each factor equal to zero and solve. The first step uses the rules for moving terms across the equals sign from the Fundamentals section.