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(8z-3)(z+5)-(8z-3)(z-4)=0
We multiply parentheses ..
(+8z^2+40z-3z-15)-(8z-3)(z-4)=0
We get rid of parentheses
8z^2+40z-3z-(8z-3)(z-4)-15=0
We multiply parentheses ..
8z^2-(+8z^2-32z-3z+12)+40z-3z-15=0
We add all the numbers together, and all the variables
8z^2-(+8z^2-32z-3z+12)+37z-15=0
We get rid of parentheses
8z^2-8z^2+32z+3z+37z-12-15=0
We add all the numbers together, and all the variables
72z-27=0
We move all terms containing z to the left, all other terms to the right
72z=27
z=27/72
z=3/8
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