Question

How do you solve $\left( x-12 \right)\left( 5x-13 \right)=0$?

Answer 1

There are two ways to solve the given equation. As we observe that there are two factors given in the equation so to solve the given equation we will equate each factor to zero. Then by solving the obtained equations we will get the values of x.

Complete step by step solution:
We have been given that $\left( x-12 \right)\left( 5x-13 \right)=0$
We have to solve the given equation and find the value of x.
Now, as the given equation has two factors equal to zero so we can directly put each factor equal to zero and by simplifying each obtained equation individually we can find the value of x. Then by equating each factor to zero we will get
$\Rightarrow \left( x-12 \right)=0$ and $\left( 5x-13 \right)=0$
Now, solving the obtained equations we will get
$\Rightarrow x=12$ and $5x=13 \Rightarrow x=\dfrac{13}{5}$

Hence on solving the given equation we get the values of $x$ as $12$ and $\dfrac{13}{5}$.

Note: Here we solve the given equation directly by equating each factor to zero. Alternatively students may solve the equation by first simplifying the given equation and converting it into quadratic form. We can solve the equation by solving the given parenthesis first. Then we will get
$\Rightarrow 5{{x}^{2}}-60x-13x+156=0$
Now, simplifying the above obtained equation we will get
$\Rightarrow 5{{x}^{2}}-73x+156=0$
Now, the above obtained equation is a quadratic equation. So we can solve the equation by using any of the methods from completing the square method, splitting the middle term method, factorization method and quadratic equation formula method.