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Question
3x^{2}+5x=-3x-4
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
More methods
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x_{1}=-2,x_{2}=-\frac{2}{3}
Alternative Form
x_{1}=-2,x_{2}=-0.\dot{6}
Evaluate
3x^{2}+5x=-3x-4
Move the expression to the left side
3x^{2}+8x+4=0
Factor the expression
More Steps
Evaluate
3x^{2}+8x+4
Rewrite the expression
3x^{2}+\left(2+6\right)x+4
Calculate
3x^{2}+2x+6x+4
Rewrite the expression
x\times 3x+x\times 2+2\times 3x+2\times 2
\text{Factor out }x\text{ from the expression}
x\left(3x+2\right)+2\times 3x+2\times 2
\text{Factor out }2\text{ from the expression}
x\left(3x+2\right)+2\left(3x+2\right)
\text{Factor out }3x+2\text{ from the expression}
\left(x+2\right)\left(3x+2\right)
\left(x+2\right)\left(3x+2\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&3x+2=0\\&x+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=-\frac{2}{3}\\&x+2=0\end{align}
\text{Solve the equation for }x
More Steps
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=-\frac{2}{3}\\&x=-2\end{align}
Solution
x_{1}=-2,x_{2}=-\frac{2}{3}
Alternative Form
x_{1}=-2,x_{2}=-0.\dot{6}
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