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\documentclass{scrartcl}
\usepackage{amsmath}
\begin{document}
\begin{alignat*}{2}
  \Sigma F_{x} \overset{!}{=}0 :&\quad&&N_{x}(x)=-A_x=0   N\\
  \Sigma F_{y}\overset{!}{=}0 :&&&Q_{y}(x)=-A_y+F+F+F-B_y\\
  \Sigma F_{z}\overset{!}{=}0 :&&& Q_{z}(x)=-A_z-B_z=0   N\\
  \Sigma M^{(S_6)}_{x}\overset{!}{=}0 :&&&M_{tx}(x)=-M_{an}+ M_{an} \cdot \frac{3}{3}\\
  \Sigma M^{(S_6)}_{y}\overset{!}{=}0 :&&&M_{by}(x)=-A_z \cdot (x-l_1)-B_z \cdot (x-(l_1+l_2+l_3+l_4))\\
  \Sigma M^{(S_6)}_{z}\overset{!}{=}0 :&&&M_{bz}(x)=
    \begin{aligned}[t]
      &A_y \cdot (x-l_1)-F \cdot (x-(l_1-l_2))\\
      &-F \cdot (x-(l_1-l_2+l_3))-F \cdot (x-(l_1-l_2+l_3+l_4))\\
      &+B_y \cdot (x-(l_1+l_2+l_3+l_4))
    \end{aligned} 
\end{alignat*} 
\end{document}

\begin{equation*}
\Sigma F_{x} \overset{!}{=}0 : \ \ \ \   N_{x}(x)=-A_x=0	N
\end{equation*}
%
\begin{equation*}
\Sigma F_{y}\overset{!}{=}0 : \ \ \ \  Q_{y}(x)=-A_y+F+F+F-B_y
\end{equation*}
%
\begin{equation*}
\Sigma F_{z}\overset{!}{=}0 : \ \ \ \ Q_{z}(x)=-A_z-B_z=0	N
\end{equation*}
%
\begin{equation*}
\Sigma M^{(S_6)}_{x}\overset{!}{=}0 : \ \ \ \ M_{tx}(x)=-M_{an}+ M_{an} \cdot \frac{3}{3}
\end{equation*}
%
\begin{equation*}
\Sigma M^{(S_6)}_{y}\overset{!}{=}0 : \ \ \ \ M_{by}(x)=-A_z \cdot (x-l_1)-B_z \cdot (x-(l_1+l_2+l_3+l_4))
\end{equation*}
%
\begin{equation*}
\begin{split}
\Sigma M^{(S_6)}_{z}\overset{!}{=}0 : \ \ \ \  M_{bz}(x)=A_y \cdot (x-l_1)-F \cdot (x-(l_1-l_2))\\-F \cdot (x-(l_1-l_2+l_3))-F \cdot (x-(l_1-l_2+l_3+l_4))+B_y \cdot (x-(l_1+l_2+l_3+l_4))
\end{split}
\end{equation*}