x^2+4=x^6+4

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x^2 + 4 = x^6 + 4Subtract 4 from both sides.x^2 = x^6Subtract x^6 from both sides.x^2 - x^6 = 0Factor out x^2.x^2(1 - x^4) = 0In parentheses is difference of squares, factor that.x^2(1 + x^2)(1 - x^2) = 0We now have the difference of two squares again with (1 - x^2), factor that.x^2(1 + x^2)(1 + x)(1 - x) = 0Now, set each factor equal to 0.x^2 = 0x = 0...1 + x^2 = 0x^2 = -1x = i...1 + x = 0x = -1...1 - x = 0x = 1