The x intercept is when y is equal to 0. So we can set the equation to 0 to find them.
(x+5)(3x+7)=0
After that, we can use the Multiplication Property of 0 to find the answers. This property says that when anything is multiplied by 0, the answer is 0. By finding the 0 of each factor, we can find the 0s of the equation because of this rule.
x+5 = 0
x = -5
3x+7 = 0
3x = -7
x = -7/3
So the x intercepts of the equation are (-5, 0) and (-7/3, 0).
