sec^2x+6tanx=-4

Solve for x, find all solutions (general solutions)
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Thank you so much if you decide to help!

sec^2 = 1 + tan^2

substituting ... tan^2(x) + 6 tan(x) + 1 = - 4
... tan^2(x) + 6 tan(x) + 5 = 0
... factoring ... [tan(x) + 5] [tan(x) + 1] = 0

tan(x) = -5 , tan(x) = -1