What 3 consecutive even integers are 3 times the sum of the first two was 58 less than 14 times the opposite of the third?

Even integers are 2 apart

they are
x,x+2,x+4

so
smallest is x, biggest is x+4

3(x+x+2)=-58+14(-1)(x+4)
simplify
3(2x+2)=-58-14(x+4)
expand
6x+6=-58-14x-56
6x+6=-14x-114
add 14x both sides
20x+6=-114
minus 6 both sides
20x=-120
divide both sides by 20
x=-6
x+2=-4
x+4=-2

de numbers are -6,-4,-2