Answer
The solution of $\left( 2{{a}^{2}}-5a+6 \right)-\left( -2{{a}^{2}}+6a-7 \right)+\left( 3{{a}^{2}}-7a-2 \right)$ is $7{{a}^{2}}-18a+11$.
Work Step by Step
Solve the brackets first,
$\begin{align}
& \left( 2{{a}^{2}}-5a+6 \right)-\left( -2{{a}^{2}}+6a-7 \right)+\left( 3{{a}^{2}}-7a-2 \right)=2{{a}^{2}}-5a+6-\left( -2{{a}^{2}} \right)-6a-\left( -7 \right)+3{{a}^{2}}-7a-2 \\
& =2{{a}^{2}}-5a+6+2{{a}^{2}}-6a+7+3{{a}^{2}}-7a-2
\end{align}$
Solve further,
$\begin{align}
& \left( 2{{a}^{2}}-5a+6 \right)-\left( -2{{a}^{2}}+6a-7 \right)+\left( 3{{a}^{2}}-7a-2 \right)=2{{a}^{2}}+2{{a}^{2}}+3{{a}^{2}}-5a-6a-7a+6+7-2 \\
& =7{{a}^{2}}-18a+11
\end{align}$
