 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that solve the equation 4x square minus 14x is equal to minus 12. We know that the zero product property says if a into b is equal to zero then either a is equal to zero or b is equal to zero. It means at least one of the factors must be zero or both can also be zero. With this key idea we shall proceed to the solution. Now we are given the quadratic equation that is 4x square minus 14x is equal to minus 12. We have to find the solution of this quadratic. We see that this equation has non-zero terms on both sides of the equal sign. So we first move minus 12 to left hand side of the equation so that we can solve it. We get 4x square minus 14x plus 12 is equal to zero. Now 2 is the common factor in all the terms so we take out 2 common and we get 2 into 2x square minus 7x plus 6 the whole is equal to zero. Now we factorize this equation and we get 2 into 2x square. Now minus 7x can be written as minus 4x minus 3x plus 6 the whole is equal to zero. This implies that 2 into now taking 2x common from first two terms we get 2x into x minus 2 the whole and now taking minus 3 common from these two terms we get minus 3 into x minus 2 the whole and this complete whole is equal to zero and this further implies that 2 into 2x minus 3 the whole into x minus 2 the whole and this complete whole is equal to zero. From the key idea we use zero product property which says if a into b is equal to zero then either a is equal to zero or b is equal to zero. This implies that 2x minus 3 is equal to zero or x minus 2 is equal to zero. We should note that here we do not consider 2 is equal to zero as 2 cannot be equal to zero. Now solving these two equations for x we get x is equal to 3 by 2 or x is equal to 2. So x is equal to 3 by 2 and x is equal to 2 are the solutions of the given equation. This is the required answer. This completes our session. Hope you enjoyed this session.