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Question
x^{2}+12x+32
Factor the expression
\left(x+4\right)\left(x+8\right)
Evaluate
x^{2}+12x+32
Rewrite the expression
x^{2}+\left(8+4\right)x+32
Calculate
x^{2}+8x+4x+32
Rewrite the expression
x\times x+x\times 8+4x+4\times 8
\text{Factor out }x\text{ from the expression}
x\left(x+8\right)+4x+4\times 8
\text{Factor out }4\text{ from the expression}
x\left(x+8\right)+4\left(x+8\right)
Solution
\left(x+4\right)\left(x+8\right)
Show Solutions
Find the roots
x_{1}=-8,x_{2}=-4
Evaluate
x^{2}+12x+32
To find the roots of the expression,set the expression equal to 0
x^{2}+12x+32=0
Factor the expression
More Steps
Evaluate
x^{2}+12x+32
Rewrite the expression
x^{2}+\left(8+4\right)x+32
Calculate
x^{2}+8x+4x+32
Rewrite the expression
x\times x+x\times 8+4x+4\times 8
\text{Factor out }x\text{ from the expression}
x\left(x+8\right)+4x+4\times 8
\text{Factor out }4\text{ from the expression}
x\left(x+8\right)+4\left(x+8\right)
\text{Factor out }x+8\text{ from the expression}
\left(x+4\right)\left(x+8\right)
\left(x+4\right)\left(x+8\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x+4=0\\&x+8=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x+4=0
Move the constant to the right-hand side and change its sign
x=0-4
Removing 0 doesn't change the value,so remove it from the expression
x=-4
\begin{align}&x=-4\\&x+8=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x+8=0
Move the constant to the right-hand side and change its sign
x=0-8
Removing 0 doesn't change the value,so remove it from the expression
x=-8
\begin{align}&x=-4\\&x=-8\end{align}
Solution
x_{1}=-8,x_{2}=-4
Show Solutions
