How do you factor and solve #t+24=t(t+6)#?

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Answer 1 · 2015-06-01T22:31:03

Subtract #t+24# from both sides to get:

#0 = t(t+6)-(t+24)#

#=t^2+6t-t-24#

#=t^2+5t-24#

#=(t+8)(t-3)#

So #t=-8# or #t=3#.

To find this factorization, I looked for a factorization of #24# into a pair of factors whose difference is #5#.