You do a problem like this by "solving it backwards",
starting with the solution and going backward to the problem.

If you had solved such an equation and ended up with

x = 7 and x = -3 

then before that you would have had

x - 7 = 0 and x + 3 = 0

then before that you would have had

(x - 7)(x + 3) = 0

then before that you would have had

x² - 4x - 21 = 0

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Check it by solving forward:

x² - 4x - 21 = 0

(x - 7)(x + 3) = 0

x - 7 = 0 and x + 3 = 0

    x = 7 and x = -3

It checks when solved forward, so the correct
equation is

x² - 4x - 21 = 0

Edwin