Question

How do you solve \[x\left( {x + 3} \right)\left( {x - 4} \right) = 0\]?

Answer 1

Hint: In this equation we have to solve the equation for \[x\], this can be done by transforming the given equation of third degree to three linear equations as a product of expressions is zero if and only if any of these expressions is zero and solve the each equation, to solve the equation take all \[x\] terms to one side and all constants to the others side and then we will get the required result.

Complete step by step solution:
Given \[x\left( {x + 3} \right)\left( {x - 4} \right) = 0\],
This is a third degree equation as the highest exponent of the variable \[x\] is equal to 3.
A product of expressions is zero if and only if any of these expressions is zero. Which means any individual factor on the left side of the equation is equal to \[0\], the entire expression will be equal to \[0\].
So, equate first term to zero, i.e.,
\[ \Rightarrow x = 0\],
Now, equate second term to zero, i.e.,
\[ \Rightarrow x + 3 = 0\],
Now subtract 3 on both sides of the equation we get,
\[ \Rightarrow x + 3 - 3 = 0 - 3\],
Now simplifying we get,
\[ \Rightarrow x = - 3\],
Now, equate third term to zero, i.e.,
\[ \Rightarrow x - 4 = 0\],
Now add 4 to both sided we get,
\[ \Rightarrow x - 4 + 4 = 0 + 4\],
Now simplifying we get,
\[ \Rightarrow x = 4\],
The final solution is all the values that make \[x\left( {x + 3} \right)\left( {x - 4} \right) = 0\] true, and they are \[x = 0, - 3,4\].

Final Answer:
\[\therefore \] The values of \[x\] when the given equation \[x\left( {x + 3} \right)\left( {x - 4} \right) = 0\] is solved will be equal to 0, -3 and 4.

Note:
A linear equation is an equation of a straight line having a maximum of one variable. The degree of the variable will be equal to 1. To solve any equation in one variable, pit all the variable terms on the left hand side and all the numerical values on the right hand side to make the calculation solved easily.