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t\left(5c+6d\right)-\left(5c+6d\right)
Do the grouping 6dt+5ct-6d-5c=\left(6dt+5ct\right)+\left(-6d-5c\right), and factor out t in the first and -1 in the second group.
\left(5c+6d\right)\left(t-1\right)
Factor out common term 5c+6d by using distributive property.