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\left(2\sqrt{2}+2\right)x=8\sqrt{2}+12
The equation is in standard form.
\frac{\left(2\sqrt{2}+2\right)x}{2\sqrt{2}+2}=\frac{8\sqrt{2}+12}{2\sqrt{2}+2}
Divide both sides by 2+2\sqrt{2}.
x=\frac{8\sqrt{2}+12}{2\sqrt{2}+2}
Dividing by 2+2\sqrt{2} undoes the multiplication by 2+2\sqrt{2}.
x=2\sqrt{2}+2
Divide 12+8\sqrt{2} by 2+2\sqrt{2}.