The equation in the question is an inequality, but the supposed solution posed in the question is for an equality:
syms x real
f(x) = -3*x^4 + 12*x^2;
solve(f(x)==0,x)
Plot f(x)
fplot(f(x),[-2 2])
So that gives us an idea of what the solution should be for f(x) > 0.
assume(x,'real') % otherwise the solver will consider x as complex
sol = solve(f(x)>0,'ReturnConditions',true);
sol.x
sol.parameters
sol.conditions
Which looks like the expected solution based on the graph.
