Question

Solve the equation $r^2-3r=4$ by factoring.

Short answer

The solution for the equation is$r=\left\{-1,4\right\}$.

Step-by-step solution

Step 1. Write down the given expression.

The given equation is $r^2-3r=4$.

Step 2. Simplify the equation.

The given equation $r^2-3r=4$ is solved as:

$\begin{array}{c}{r}^2-3r=\mathrm{4....}\left(\text{Given}\right)\\ r^2-3r-4=\mathrm{0....}\left(\text{Re-arrange}\right)\\ \left(r-4\right)\left(r+1\right)=\mathrm{0....}\left(\text{Factoring}\right)\\ r-4=0\text{or}r+1=0\\ r=4\text{or}r=-1\\ r=\left\{-1,4\right\}\end{array}$

Step 3. Conclusion.

The solution for the given equation is $r=\left\{-1,4\right\}$.