SOLUTION: the sum of ages of two children is 12 and their product is 32.the age of elder one? please complete solution

Let x be the age of the older child. 
Then the age of the younger is 12 -x,

and the product is 

x*(12-x) = 32.

Transform it into the quadratic equation

 = .

Factor the left side:

(x-4)*(x-8) = 0.

The solutions are x = 4 and x = 8.

The elder child age is 8 years.