How do you factor the expression \[3{{x}^{2}}+2x-1=0\]?

Hint: In this problem we have to factorize the given quadratic equation. We can split the coefficient of x term we will get four terms in the equation. We can separate the terms into two pairs and take common terms outside to get the factors of the given equation. We can also use the quadratic method formula to find the factors of the given quadratic equation.

Complete step by step answer:
We know that the given quadratic equation to be factored is,
 \[3{{x}^{2}}+2x-1=0\]…… (1)
We can take the coefficient of x term and split it, we get
\[\Rightarrow 2x=3x-1x\]
We can write the above step in the given quadratic equation (1), we get
\[\Rightarrow 3{{x}^{2}}+3x-x-1=0\]
Now we can take the common terms from the first two terms and the last two terms.
\[\Rightarrow 3x\left( x+1 \right)-1\left( x+1 \right)\]
We know that in the above step, we have a common terms x+1, which we can take outside and write the remaining term, we get
\[\Rightarrow \left( x+1 \right)\left( 3x-1 \right)\]
Therefore, the factors of the given quadratic equation \[3{{x}^{2}}+2x-1=0\] is \[\left( x+1 \right)\left( 3x-1 \right)\].

Note:
Students make mistakes while splitting the middle term, that is the coefficient of x terms which should be concentrated. We can also use the quadratic method formula to check for the correct factors. Here, we have a coefficient for square of x, so we can divide that in the equation and can take the constant term, which is multiplied by numbers to get the same value and add/subtract to get the coefficient of x.