 Hello and welcome to the session. In this session we will discuss the following question and the question says 12 x squared minus 5x plus 6 is equal to 0. Let's start the solution now. We are given the quadratic equations x squared minus 5x plus 6 is equal to 0. We will solve it by factorizing. For this, first we will split the middle term. We have the quadratic equation x squared minus 5x plus 6 is equal to 0. And middle term is minus 5x. We will split it into two terms such that the product of the two terms is equal to the product of the first and the last term of the quadratic equation. Now minus 5x can be written as minus 3x minus 2x and the product of these two terms that is minus 3x into minus 2x which is equal to 6x squared. Now this is equal to x squared which is the first term into 6 which is the last term of the quadratic equation. So we can see that the product of the middle terms is equal to the product of first and last term of the quadratic equation. So the middle term that is minus 5x can be split into minus 3x minus 2x. So this implies after splitting the middle term we get x squared minus 2x minus 3x plus 6 is equal to 0. Now we will factorize it. So this implies taking x common between the first and the second term we get x into x minus 2 the whole. Now taking minus 3 common between the last two terms we have minus 3 into x minus 2 the whole is equal to 0. This implies x minus 2 the whole into x minus 3 the whole is equal to 0. So we have factorized the given quadratic equation into two factors. This implies x minus 2 is equal to 0 or x minus 3 is equal to 0. This implies from the first equation we get x is equal to 2 or from the second equation we get x is equal to 3. So these are the two possible solutions of the given quadratic equation. Now we will check if these two values x satisfy the given equation. First we will substitute x is equal to 2 in the given quadratic equation. So we get the left hand side becomes 2 square minus 5 into 2 plus 6. This is equal to x minus 10 plus 6 which is equal to 10 minus 10 which is equal to 0. This is equal to the right hand side of the quadratic equation. So x is equal to 2 satisfies the given quadratic equation. Now we will check for x is equal to 3 so we will substitute x is equal to 3 in the given quadratic equation. So the left hand side becomes 3 square minus 5 into 3 plus 6. This is equal to 9 minus 15 plus 6 which is equal to 15 minus 15. This is equal to 0 which is equal to the right hand side of the quadratic equation. So x is equal to 3 also satisfies the given quadratic equation. So we can say that the final answer is x is equal to 2 and x is equal to 3. With this we end our session. Hope you enjoyed the session.