0=(t-6)*(-2t*-2t+3t-6)

Question

The - 2t*-2t is the same as saying -2t(squared)

Answer 1

0=(t-6)((-2t)²+3t-6) clearly has a solution t=6, because t-6=0 satisfies the equation.

(-2t)²+3t-6 = 4t²+3t-6=4(t²+¾t-3/2).

t²+¾t-3/2 can be written: t²+¾t+9/64-9/64-3/2=

(t+⅜)²-(9/64+96/64).

When this is equal to 0 we get more solutions for t.

(t+⅜)²-(9/64+96/64)=0,

(t+⅜)²-105/64=0, (t+⅜)²=105/64,

t+⅜=±√105/8,

so t=-⅜±√105/8=-0.375±10.24695/8=

-0.375±1.28087 giving us t=0.9059 and -1.6559 approx.

So the total solution is t=-1.6559, 0.9059 or 6.