Algebra 1 homework help please

I am so horrible at math and right now I am being homeschooled so no one can really help me with my math. So if you could help out a bit that would be amazing. So the problem is: Find three consecutive even integers such that the sum of the squares of the smaller two is equal to the square of the largest.

Could you explain to me step by step of how to do this? Thank you. :)

if u assume the first number ix x then the next number will be (x+2) annd the next one (x+4)
so x^2+(x+2)^2=(x+4)^2
x^2+x^2+4x+4=x^2+8x+16
2x^2+4x+4=x^2+8x+16
x^2-4x-12=0 (x-6)(x+2)=0
x-6=0 x=6 x=-2 not acceptable
(X+2)=8 (x+4)=10

this is a Pythagorean Theorem type. basically it wants a right triangle where a^2 + b^2 = c^2
there are many different forms of it, but a common one is 3, 4, 5
3^2 + 4^2 = 5^2
9 + 16 = 25
25=25

2x , 2x + 2 , 2x + 4

4x ² + ( 2x + 2 ) ² = ( 2x + 4 ) ²

4x ² + 4 x ² + 8x + 4 = 4x ² + 16x + 16

4 x ² - 8x - 12 = 0

x ² - 2x - 3 = 0

( x - 3 ) ( x + 1 ) = 0

x = 3 is acceptable

Integers are then 6 , 8 and 10

a , a + 2 , a + 4
a^2 + a^2 + 4a + 4 = a^2 + 8a + 16
a^2 - 4a - 12 = 0
(a - 6)(a + 2) = 0
a = 6 , 8 , 10