Can an equation have equal expressions

I’ve been trying all day to figure this puzzle out. i need the work for it aswell. it is a factoring polynomials tarsia. the image is below.

If t8 = 4 and t12 = −2, find the first three terms of the arithmetic sequence.

Cole says the distance between points (-5,0) and (0,-5)is 5 units. is he correct? explain why or why not.