Question: How to cancel a common factor in two of three terms?

I have the following expression which is a sum of three terms.  The first term has a -(H1+H2)^2 and the second one has a (H1+H2)^2 term and I would like to simplify this by dividing the equation by (H1+H2)^2 but I can't figure out how to force maple to do that.  Any help would be greatly appreciated.

(-2*H1*H2-H2^2-H1^2)*`ϕt`+(H1^2+2*H1*H2+H2^2)*`ηt`*Ut+4*H2*H1*Uc*`ηc` = 0

Also, f someone can direct me to where I can learn to present equations better in this file that would be icing on the cake.

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