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Question
3x^{2}-x-2
Factor the expression
\left(x-1\right)\left(3x+2\right)
Evaluate
3x^{2}-x-2
Rewrite the expression
3x^{2}+\left(2-3\right)x-2
Calculate
3x^{2}+2x-3x-2
Rewrite the expression
x\times 3x+x\times 2-3x-2
\text{Factor out }x\text{ from the expression}
x\left(3x+2\right)-3x-2
\text{Factor out }-1\text{ from the expression}
x\left(3x+2\right)-\left(3x+2\right)
Solution
\left(x-1\right)\left(3x+2\right)
Show Solutions
Find the roots
x_{1}=-\frac{2}{3},x_{2}=1
Alternative Form
x_{1}=-0.\dot{6},x_{2}=1
Evaluate
3x^{2}-x-2
To find the roots of the expression,set the expression equal to 0
3x^{2}-x-2=0
Factor the expression
More Steps
Evaluate
3x^{2}-x-2
Rewrite the expression
3x^{2}+\left(2-3\right)x-2
Calculate
3x^{2}+2x-3x-2
Rewrite the expression
x\times 3x+x\times 2-3x-2
\text{Factor out }x\text{ from the expression}
x\left(3x+2\right)-3x-2
\text{Factor out }-1\text{ from the expression}
x\left(3x+2\right)-\left(3x+2\right)
\text{Factor out }3x+2\text{ from the expression}
\left(x-1\right)\left(3x+2\right)
\left(x-1\right)\left(3x+2\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-1=0\\&3x+2=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
\begin{align}&x=1\\&3x+2=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
3x+2=0
Move the constant to the right-hand side and change its sign
3x=0-2
Removing 0 doesn't change the value,so remove it from the expression
3x=-2
Divide both sides
\frac{3x}{3}=\frac{-2}{3}
Divide the numbers
x=\frac{-2}{3}
\text{Use }\frac{-a}{b}=\frac{a}{-b}=-\frac{a}{b}\text{ to rewrite the fraction}
x=-\frac{2}{3}
\begin{align}&x=1\\&x=-\frac{2}{3}\end{align}
Solution
x_{1}=-\frac{2}{3},x_{2}=1
Alternative Form
x_{1}=-0.\dot{6},x_{2}=1
Show Solutions
