I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 2.5 : Quadratic Equations - Part I
7. Solve the following quadratic equation by factoring.
\[12{x^2} = 25x\]Show All Steps Hide All Steps
Start SolutionThe first thing we need to do is get everything on one side of the equation and then factor the quadratic.
\[\begin{align*}12{x^2} - 25x & = 0\\ x\left( {12x - 25} \right) & = 0\end{align*}\]Make sure that you do not just cancel an \(x\) from both sides of the equation!
Show Step 2Now all we need to do is use the zero factor property to get,
\[\begin{array}{*{20}{c}}{x = 0}\\{}\end{array}\hspace{0.25in}{\mbox{OR}}\hspace{0.25in}\begin{array}{*{20}{c}}{12x - 25 = 0}\\{\displaystyle x = \frac{{25}}{{12}}}\end{array}\]Therefore the two solutions are : \(\require{bbox} \bbox[2pt,border:1px solid black]{{x = 0\,\,{\mbox{and }}x = \frac{{25}}{{12}}}}\)
Note that if we’d canceled an \(x\) from both sides of the equation in the first step we would have missed the solution \(x = 0\)!