# How do you solve 3t(t+5)-t^2=2t^2+4t-1?

May 6, 2016

Expand and simplify to find:

$t = - \frac{1}{11}$

#### Explanation:

Expanding the left hand side we find:

$3 t \left(t + 5\right) - {t}^{2} = 3 {t}^{2} + 15 t - {t}^{2} = 2 {t}^{2} + 15 t$

So the equation becomes:

$2 {t}^{2} + 15 t = 2 {t}^{2} + 4 t - 1$

Subtract $2 {t}^{2}$ from both sides to get:

$15 t = 4 t - 1$

Subtract $4 t$ from both sides to get:

$11 t = - 1$

Divide both sides by $11$ to get:

$t = - \frac{1}{11}$