1. **Problem Statement:** Solve the equation by applying the condition of equality of complex numbers. 2. **Key Concept:** Two complex numbers $a+bi$ and $c+di$ are equal if and only if their real parts are equal and their imaginary parts are equal, i.e., $a=c$ and $b=d$. 3. **Example Problem:** Solve for $x$ if $3 + 2xi = 5 + (4 - x)i$. 4. **Step 1:** Equate the real parts: $$3 = 5$$ This is not true, so check if the problem might have a typo or if $x$ affects the real part. 5. **Step 2:** Equate the imaginary parts: $$2x = 4 - x$$ 6. **Step 3:** Solve for $x$: $$2x + x = 4$$ $$3x = 4$$ $$x = \frac{4}{3}$$ 7. **Step 4:** Since the real parts are not equal, the original equation has no solution unless the real parts are equal. If the problem is to find $x$ such that the imaginary parts are equal, then $x=\frac{4}{3}$. **Final answer:** $x=\frac{4}{3}$ (assuming equality of imaginary parts only).