Solve for u. (3)/(2)=-(7)/(5)u-(7)/(6) Simplify your answer as much as possible. u= square

To solve for \( u \) in the equation <br /><br />\[<br />\frac{3}{2} = -\frac{7}{5}u - \frac{7}{6},<br />\]<br /><br />we follow these steps:<br /><br />1. **Isolate the term involving \( u \)**:<br /> \[<br /> \frac{3}{2} + \frac{7}{6} = -\frac{7}{5}u.<br /> \]<br /><br />2. **Find a common denominator to combine the fractions on the left side**:<br /> The least common multiple of 2 and 6 is 6. So, we rewrite \(\frac{3}{2}\) with a denominator of 6:<br /> \[<br /> \frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}.<br /> \]<br /> Now, add \(\frac{9}{6}\) and \(\frac{7}{6}\):<br /> \[<br /> \frac{9}{6} + \frac{7}{6} = \frac{9 + 7}{6} = \frac{16}{6} = \frac{8}{3}.<br /> \]<br /> So the equation becomes:<br /> \[<br /> \frac{8}{3} = -\frac{7}{5}u.<br /> \]<br /><br />3. **Solve for \( u \)**:<br /> Multiply both sides by the reciprocal of \(-\frac{7}{5}\), which is \(-\frac{5}{7}\):<br /> \[<br /> u = \frac{8}{3} \times -\frac{5}{7} = -\frac{8 \times 5}{3 \times 7} = -\frac{40}{21}.<br /> \]<br /><br />Thus, the simplified solution for \( u \) is:<br />\[<br />u = -\frac{40}{21}.<br />\]