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±4,±2,±1
By Rational Root Theorem, all rational roots of a polynomial are in the form \frac{p}{q}, where p divides the constant term -4 and q divides the leading coefficient 1. List all candidates \frac{p}{q}.
t=-2
Find one such root by trying out all the integer values, starting from the smallest by absolute value. If no integer roots are found, try out fractions.
t^{2}-2t-2=0
By Factor theorem, t-k is a factor of the polynomial for each root k. Divide t^{3}-6t-4 by t+2 to get t^{2}-2t-2. Solve the equation where the result equals to 0.
t=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 1\left(-2\right)}}{2}
All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Substitute 1 for a, -2 for b, and -2 for c in the quadratic formula.
t=\frac{2±2\sqrt{3}}{2}
Do the calculations.
t=1-\sqrt{3} t=\sqrt{3}+1
Solve the equation t^{2}-2t-2=0 when ± is plus and when ± is minus.
t=-2 t=1-\sqrt{3} t=\sqrt{3}+1
List all found solutions.