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

Jun 1, 2015

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

$0 = t \left(t + 6\right) - \left(t + 24\right)$

$= {t}^{2} + 6 t - t - 24$

$= {t}^{2} + 5 t - 24$

$= \left(t + 8\right) \left(t - 3\right)$

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 $5$.