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Question
3x^{2}-5x=6-2x
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
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x_{1}=-1,x_{2}=2
Evaluate
3x^{2}-5x=6-2x
Move the expression to the left side
3x^{2}-3x-6=0
Factor the expression
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Evaluate
3x^{2}-3x-6
Rewrite the expression
3x^{2}-3x-3\times 2
\text{Factor out }3\text{ from the expression}
3\left(x^{2}-x-2\right)
Factor the expression
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Evaluate
x^{2}-x-2
Rewrite the expression
x^{2}+\left(1-2\right)x-2
Calculate
x^{2}+x-2x-2
Rewrite the expression
x\times x+x-2x-2
\text{Factor out }x\text{ from the expression}
x\left(x+1\right)-2x-2
\text{Factor out }-2\text{ from the expression}
x\left(x+1\right)-2\left(x+1\right)
\text{Factor out }x+1\text{ from the expression}
\left(x-2\right)\left(x+1\right)
3\left(x-2\right)\left(x+1\right)
3\left(x-2\right)\left(x+1\right)=0
Divide the terms
\left(x-2\right)\left(x+1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-2=0\\&x+1=0\end{align}
\text{Solve the equation for }x
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Evaluate
x-2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
\begin{align}&x=2\\&x+1=0\end{align}
\text{Solve the equation for }x
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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=2\\&x=-1\end{align}
Solution
x_{1}=-1,x_{2}=2
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