ANSWER
Eric is
[tex]35years[/tex]
EXPLANATION
Let Eric's age be
[tex]x \: \: years[/tex]
Then his son age will be,
[tex](x - 30) \: years[/tex]
The product of their ages is 175.
This implies that,
[tex]x(x - 30) = 175[/tex]
We expand to get,
[tex]x^2- 30x = 175[/tex]
We equate everything to zero to obtain,
[tex] {x}^{2} - 30x - 175 = 0[/tex]
We split the middle term to get,
[tex] {x}^{2} +5x- 35x - 175 = 0[/tex]
We factor to obtain,
[tex] x(x +5)- 35(x +5) = 0[/tex]
We factor further to get,
[tex](x - 35)( x + 5) = 0[/tex]
This implies that,
[tex]x = 35 \: or \: - 5[/tex]
Since age is not negative,
[tex]x = 35years[/tex]
Therefore Eric is
[tex]35years[/tex]
