Solve for \( u \). \( \begin{array}{l}-2 u=\frac{4}{3}(3 u+6)-2\left(3+\frac{5}{2} u\right) \\ u=\square\end{array} \)

To solve for \( u \) in the equation: \[ -2u = \frac{4}{3}(3u + 6) - 2\left(3 + \frac{5}{2}u\right) \] **Step 1: Expand and Simplify Both Sides** First, expand the right-hand side of the equation: \[ \frac{4}{3}(3u + 6) = \frac{4}{3} \times 3u + \frac{4}{3} \times 6 = 4u + 8 \] \[ -2\left(3 + \frac{5}{2}u\right) = -2 \times 3 - 2 \times \frac{5}{2}u = -6 - 5u \] Now, substitute these back into the original equation: \[ -2u = 4u + 8 - 6 - 5u \] Combine like terms on the right-hand side: \[ 4u - 5u + 8 - 6 = -u + 2 \] So, the equation simplifies to: \[ -2u = -u + 2 \] **Step 2: Solve for \( u \)** To isolate \( u \), follow these steps: 1. **Add \( 2u \) to both sides:** \[ -2u + 2u = -u + 2 + 2u \] \[ 0 = u + 2 \] 2. **Subtract 2 from both sides:** \[ 0 - 2 = u + 2 - 2 \] \[ -2 = u \] **Solution:** \[ u = -2 \]