How do you simplify\[3{{x}^{3}}+3{{x}^{2}}\]?

Hint: This question belongs to the topic of algebra. We should know how to find the equations and how to solve the equation or how to factor the given equation. And, we should know how to find the factors of any given. In this question, we will find the factors of the given equation\[3{{x}^{3}}+3{{x}^{2}}\].

Complete step by step answer:
Let us solve this question.
In this question, we have asked to simplify the equation or to factorize the given equation. In this question, the given equation is
\[3{{x}^{3}}+3{{x}^{2}}\]
The above equation can also be written as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3\times x\times x\times x+3\times x\times x\]
We can see that in the above equation, 3 is a common factor there.
So, we can write the above equation as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3\left( x\times x\times x+x\times x \right)\]
We can see in the above equation that there is x which is a common factor in the above equation. So, we can write the above equation as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3\times x\left( x\times x+x \right)\]
We can write the above equation as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3x\left( x\times x+x \right)\]
Now, in the parenthesis or bracket of the right side of the equation, we can see that there is another common factor as x. So, we can take out x as a common factor from that parenthesis or bracket.
So, after taking out the common factor x, we can write the above equation as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3x\times x\left( x+1 \right)\]
As we know that \[x\times x\] can be written as \[{{x}^{2}}\].
So, the above equation can also be written as
\[\Rightarrow 3{{x}^{3}}+3{{x}^{2}}=3{{x}^{2}}\left( x+1 \right)\]
Hence, we have found that \[3{{x}^{3}}+3{{x}^{2}}\] can be written as \[3{{x}^{2}}\left( x+1 \right)\].
So, we can say that the simplification or the simplified value or the factors of \[3{{x}^{3}}+3{{x}^{2}}\] is \[3{{x}^{2}}\left( x+1 \right)\].

Note:
For solving these types of questions, we should have a better knowledge of the topic of algebra. So that we can find the factors easily. If we have to simplify the value of \[3{{x}^{3}}+3{{x}^{2}}\]. Then, we will equate this equation to zero.
\[3{{x}^{3}}+3{{x}^{2}}=0\]
The above equation can also be written as
\[\Rightarrow 3{{x}^{2}}\left( x+1 \right)=0\]
Hence, from here we can find the values of x.
x+1=0 and x=0
so, the value of x are 0 and -1.