Question

How do you solve $\left( {7x + 3} \right)\left( {2x - 6} \right) = 0$?

Answer 1

Hint: Given an expression. We have to find the value of the expression. First, we will set each factor equal to zero. Then solve the equation for x. Write the solution of the equation.

Complete step by step solution:
We are given the expression, $\left( {7x + 3} \right)\left( {2x - 6} \right) = 0$. First, set each factor equal to zero.
$ \Rightarrow \left( {7x + 3} \right) = 0{\text{ or }}\left( {2x - 6} \right) = 0$
Solve the first factor for x.
$ \Rightarrow 7x + 3 = 0$
Now, we will subtract 3 from both sides of the equation.
$ \Rightarrow 7x + 3 - 3 = 0 - 3$
$ \Rightarrow 7x = - 3$
Divide both sides of the equation by $7$.
$ \Rightarrow \dfrac{{7x}}{7} = \dfrac{{ - 3}}{7}$
$ \Rightarrow x = - \dfrac{3}{7}$
Solve the second factor for x.
$ \Rightarrow 2x - 6 = 0$
Now, we will add 6 to both sides of the equation.
$ \Rightarrow 2x - 6 + 6 = 0 + 6$
$ \Rightarrow 2x = 6$
Divide both sides of the equation by $2$.
$ \Rightarrow \dfrac{{2x}}{2} = \dfrac{6}{2}$
$ \Rightarrow x = 3$

Hence, the solution of the expression is equal to $x = - \dfrac{3}{7}$ or $x = 3$

Additional Information:
The factorization of the quadratic equation can be done in many ways such as factorization by splitting the middle term. Then, take out the common terms and find the factors of the equation. Then, set each factor equal to zero and solve the equation for the variable. Another method to factorize the equation is by completing the square if it is not possible to apply the algebraic identity directly to the equation. Then each factor will set equal to zero in order to solve for the equation for the variable. Then, apply the basic arithmetic operations to solve the equation.

Note:
In such types of questions students mainly do mistakes while applying the algebraic identity. Students may get confused on which algebraic identity must be applied. In such types of questions, students can also make calculation mistakes while solving for the variable.