Question

Solve the equation $18u^2-3u=1$ by factoring.

Short answer

The solution for the equation is $u=\left\{-\frac{1}{6},\frac{1}{3}\right\}$.

Step-by-step solution

Step 1. Write down the given expression.

The given equation is $18u^2-3u=1$.

Step 2. Simplify the equation.

The given equation $18u^2-3u=1$ is solved as:

$\begin{array}{c}18u^2-3u=\mathrm{1....}\left(\text{Given}\right)\\ 18u^2-3u-1=\mathrm{0....}\left(\text{Re-arrange}\right)\\ 18u^2-6u+3u-1=0\\ 6u\left(3u-1\right)+1\left(3u-1\right)=\mathrm{0....}\left(\text{Factoring}\right)\\ \left(6u+1\right)\left(3u-1\right)=0\\ 6u+1=0\text{or}3u-1=0\\ u=-\frac{1}{6}\text{or}u=\frac{1}{3}\\ u=\left\{-\frac{1}{6},\frac{1}{3}\right\}\end{array}$

Step 3. Conclusion.

The solution for the given equation is $u=\left\{-\frac{1}{6},\frac{1}{3}\right\}$.