(1) Divide through by 8: 8x³+1=0; a³+b³=(a+b)(a²-ab+b²); let a=2x, b=1 then (2x+1)(4x²-2x+1)=0; 2x+1=0, x=-½; or
4x²-2x+1=0⇒x=(2±√(4-16))/8, x=(1±i√3)/4. Three roots: -½, ¼+i√3/4 or ¼-√3/4.
(2) x⁴-10x²+9=0 (assumed), (x²-9)(x²-1)=(x-3)(x+3)(x-1)(x+1), x=-3, -1, 1 or 3.
(3) (x²-4)²=0=(x-2)(x+2), x=-2 or 2.
(4) x⁴-12x²-64=0=(x²-16)(x²+4)=(x-4)(x+4)(x+2i)(x-2i); x=-4, 4, -2i or 2i.
(5) x⁴+7x²-18=0=(x²+9)(x²-2)=(x-3i)(x+3i)(x-√2)(x+√2); x=-3, 3, -√2 or √2.
(6) x⁴+4x²-12=0=(x²+6)(x²-2)=(x-i√6)(x+i√6)(x-√2)(x+√2); x=-√2, √2, -i√6 or -i√6.