find all the real solutions, if any, of each equation.2x^3 =3x^210a^2x^2 - 2abx - 36b^2 = 0

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For the first line divide both sides by x^2. 2x = 3 x=3/2=1.5 For the second line the minus sign for 36b^2 means the factors are opposite signs.  The minus sign for the 2abx portion means the factors forming the largest product will have the negative sign.  The factors of 10a^2x^2 are 2ax and 5ax.  The factors of 36b^2 are 4b and 9b.  Because of the foil process the 4b*5ax =20abx and 2ax*9b =18abx which gives the needed center term with a 2abx if subtracted so 4b gets the negative sign (2ax-4b)(5ax+9b)=0 is the factored form. Solving for x we have 2ax-4b = 0 2ax=4b x=4b/2a      The first answer For the second factor we have 5ax + 9b = 0 5ax=-9b x = -9b/5a    The second answer.