SOLUTION: Help me solve this polynomial equation algebraically: (12x^4) - (3x^2)

SOLUTION: Help me solve this polynomial equation algebraically: (12x^4) - (3x^2) - 54 = 0

Question 717596: Help me solve this polynomial equation algebraically:
(12x^4) - (3x^2) - 54 = 0
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Divide left and right members by 3. Substitute for x^2 as a different single variable and solve for that variable; and then reverse the subsitution to continue solving for x.

Your equation is the same as .

You could ignore the substitution for x^2 suggestion and go along with x^2 as the variable, and THEN continue on for x. The simpler equation on the left side is factorable, so you now have .

For x^2+2=0, no real solution. Complex solution yes. No real one. or .

For 4x^2-9=0, 4x^2=9, x^2=9/4, or .
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