How do you solve 12/t+t-8=0?

Dec 1, 2017

$t = 6 \mathmr{and} t = 2$

Explanation:

You have equation with a fraction. You can get rid of the denominator by multiplying each term by $t$

$\frac{\textcolor{b l u e}{t \times} 12}{t} + \textcolor{b l u e}{t \times} t - \textcolor{b l u e}{t \times} \left(8\right) = 0 \times t$

$12 + {t}^{2} - 8 t = 0 \text{ } \leftarrow$ re-arrange the terms

${t}^{2} - 8 t + 12 = 0 \text{ } \leftarrow$ factorise

$\left(t - 6\right) \left(t - 2\right) = 0$

Set each factor equal to $0$

$t - 6 = 0 \text{ } \rightarrow t = 6$

$t - 2 = 0 \text{ } \rightarrow t = 2$