Please help! Go into as much detail as you possibly can! I really need help with the entire topic of Linear Equations. Thank you!

It's basically a straightforward order of operations question, with a lot of nested parentheses (ie, parentheses within parentheses) to confuse you. With nested parentheses, always start from the innermost.

2[ 3 - 5(z - 7)] = 8(5z - 8)

2[3 - 5z + 35] = 8(5z - 8) [distributed -5 over the binomial (z - 7)]

6 - 10z + 70 = 8(5z - 8) [distributed 2 over the trinomial (3 - 5z + 35)]

6 - 10z + 70 = 40z - 64 [distributed 8 over the binomial (5z - 8)]

76 - 10z = 40z - 64 [arithmetic combination of the left side]

76 = 50z -64 [added 10z to both sides]

140 = 50z [added 64 to both sides]

2.8 = z [divided both sides by 50]

z = 2.8 [flipped the equality around]

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