Need assistance with solving sextic (degree 6 polynomial) equation

Find all real numbers of x which satisfy the equation

(1+x)^6-2(1-x)^6=(1-x^2)^3

Please help.

Student X

(1+x)^6-2(1-x)^6=(1-x^2)^3 

(1+x)^6-2(1-x)^6=(1-x)^3 * (1+x)^3 -----------(1) 

Let a=(1+x)^3, b=(1-x)^3, then (1) becomes   a^2 -2b^2 = ab

Migrating all terms to the LHS,  

a^2 -ab -2b^2 =0 

(a-2b)(a+b) =0 

a=2b or a=b 

Resubstitute the expressions for both a and b in terms of x, you should arrive at the required answers shortly. Peace.

Best Regards, 

Mr Koh