Cancel \(\sqrt{3}\) on both sides.
\[\sqrt{2}=a\sqrt{2}+b\sqrt{3}+\sqrt{6}+d\times 4\]
Regroup terms.
\[\sqrt{2}=\sqrt{2}a+b\sqrt{3}+\sqrt{6}+d\times 4\]
Regroup terms.
\[\sqrt{2}=\sqrt{2}a+\sqrt{3}b+\sqrt{6}+d\times 4\]
Regroup terms.
\[\sqrt{2}=\sqrt{2}a+\sqrt{3}b+\sqrt{6}+4d\]
Subtract \(\sqrt{3}b\) from both sides.
\[\sqrt{2}-\sqrt{3}b=\sqrt{2}a+\sqrt{6}+4d\]
Subtract \(\sqrt{6}\) from both sides.
\[\sqrt{2}-\sqrt{3}b-\sqrt{6}=\sqrt{2}a+4d\]
Subtract \(4d\) from both sides.
\[\sqrt{2}-\sqrt{3}b-\sqrt{6}-4d=\sqrt{2}a\]
Divide both sides by \(\sqrt{2}\).
\[\frac{\sqrt{2}-\sqrt{3}b-\sqrt{6}-4d}{\sqrt{2}}=a\]
Simplify \(\frac{\sqrt{2}-\sqrt{3}b-\sqrt{6}-4d}{\sqrt{2}}\) to \(1+\frac{-\sqrt{3}b-\sqrt{6}-4d}{\sqrt{2}}\).
\[1+\frac{-\sqrt{3}b-\sqrt{6}-4d}{\sqrt{2}}=a\]
Switch sides.
\[a=1+\frac{-\sqrt{3}b-\sqrt{6}-4d}{\sqrt{2}}\]
a=1+(-sqrt(3)*b-sqrt(6)-4*d)/sqrt(2)
