Find all values of $t$ that satisfy $\dfrac{t+4}{t+5} = \dfrac{t-5}{2t}$. If you find more than one, then list the values separated by commas. If the solutions are not real, then they should be written in $a + bi$ form.
+36916 (t+4)/(t+5) = (t-5)/2t multiply through by 2t(t+5)
2t( t+4) = (t-5)(t+5)
2t^2 + 8t = t^2 - 25 re-arrange
t^2 + 8t + 25 = 0 Use quadratic formula to find t = -4 +- 3i
+36916 (t+4)/(t+5) = (t-5)/2t multiply through by 2t(t+5)
2t( t+4) = (t-5)(t+5)
2t^2 + 8t = t^2 - 25 re-arrange
t^2 + 8t + 25 = 0 Use quadratic formula to find t = -4 +- 3i
