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Question
6a^{2}+9a-27
Factor the expression
3\left(a+3\right)\left(2a-3\right)
Evaluate
6a^{2}+9a-27
Rewrite the expression
3\times 2a^{2}+3\times 3a-3\times 9
\text{Factor out }3\text{ from the expression}
3\left(2a^{2}+3a-9\right)
Solution
More Steps
Evaluate
2a^{2}+3a-9
Rewrite the expression
2a^{2}+\left(-3+6\right)a-9
Calculate
2a^{2}-3a+6a-9
Rewrite the expression
a\times 2a-a\times 3+3\times 2a-3\times 3
\text{Factor out }a\text{ from the expression}
a\left(2a-3\right)+3\times 2a-3\times 3
\text{Factor out }3\text{ from the expression}
a\left(2a-3\right)+3\left(2a-3\right)
\text{Factor out }2a-3\text{ from the expression}
\left(a+3\right)\left(2a-3\right)
3\left(a+3\right)\left(2a-3\right)
Show Solutions
Find the roots
a_{1}=-3,a_{2}=\frac{3}{2}
Alternative Form
a_{1}=-3,a_{2}=1.5
Evaluate
6a^{2}+9a-27
To find the roots of the expression,set the expression equal to 0
6a^{2}+9a-27=0
Factor the expression
More Steps
Evaluate
6a^{2}+9a-27
Rewrite the expression
3\times 2a^{2}+3\times 3a-3\times 9
\text{Factor out }3\text{ from the expression}
3\left(2a^{2}+3a-9\right)
Factor the expression
More Steps
Evaluate
2a^{2}+3a-9
Rewrite the expression
2a^{2}+\left(-3+6\right)a-9
Calculate
2a^{2}-3a+6a-9
Rewrite the expression
a\times 2a-a\times 3+3\times 2a-3\times 3
\text{Factor out }a\text{ from the expression}
a\left(2a-3\right)+3\times 2a-3\times 3
\text{Factor out }3\text{ from the expression}
a\left(2a-3\right)+3\left(2a-3\right)
\text{Factor out }2a-3\text{ from the expression}
\left(a+3\right)\left(2a-3\right)
3\left(a+3\right)\left(2a-3\right)
3\left(a+3\right)\left(2a-3\right)=0
Divide the terms
\left(a+3\right)\left(2a-3\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&a+3=0\\&2a-3=0\end{align}
\text{Solve the equation for }a
More Steps
Evaluate
a+3=0
Move the constant to the right-hand side and change its sign
a=0-3
Removing 0 doesn't change the value,so remove it from the expression
a=-3
\begin{align}&a=-3\\&2a-3=0\end{align}
\text{Solve the equation for }a
More Steps
Evaluate
2a-3=0
Move the constant to the right-hand side and change its sign
2a=0+3
Removing 0 doesn't change the value,so remove it from the expression
2a=3
Divide both sides
\frac{2a}{2}=\frac{3}{2}
Divide the numbers
a=\frac{3}{2}
\begin{align}&a=-3\\&a=\frac{3}{2}\end{align}
Solution
a_{1}=-3,a_{2}=\frac{3}{2}
Alternative Form
a_{1}=-3,a_{2}=1.5
Show Solutions
