# How do you solve 7(t^2+5t-9)+t=t(7t-2)+13?

May 27, 2017

#### Answer:

$t = 2$

#### Explanation:

$\text{the first step is to distribute the brackets on both sides}$

$\Rightarrow 7 {t}^{2} + 35 t - 63 + t = 7 {t}^{2} - 2 t + 13$

$7 {t}^{2} + 36 t - 63 = 7 {t}^{2} - 2 t + 13 \leftarrow \text{ simplify left side}$

$\text{collect variables on left and numeric values on right}$

$\cancel{7 {t}^{2}} \cancel{- 7 {t}^{2}} + 36 t + 2 t = 13 + 63$

$\Rightarrow 38 t = 76$

$\text{divide both sides by 38}$

$\frac{\cancel{38} \textcolor{w h i t e}{x} t}{\cancel{38}} = \frac{76}{38}$

$\Rightarrow t = 2$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if both sides equate then it is the solution.

$\text{left } = 7 \left(4 + 10 - 9\right) + 2 = \left(7 \times 5\right) + 2 = 37$

$\text{right } = 2 \left(14 - 2\right) + 13 = \left(2 \times 12\right) + 13 = 37$

$\Rightarrow t = 2 \text{ is the solution}$