Solve For Y Bd6482

1. **State the problem:** We need to express $y$ as the subject of the formula given the equation $$4x = 5 \sqrt[3]{6y - 2p}$$. 2. **Isolate the cube root term:** Divide both sides by 5 to isolate the cube root. $$\frac{4x}{5} = \sqrt[3]{6y - 2p}$$ 3. **Eliminate the cube root:** Cube both sides to remove the cube root. $$\left(\frac{4x}{5}\right)^3 = 6y - 2p$$ 4. **Expand the cube:** $$\frac{(4x)^3}{5^3} = 6y - 2p$$ $$\frac{64x^3}{125} = 6y - 2p$$ 5. **Isolate $y$:** Add $2p$ to both sides. $$6y = \frac{64x^3}{125} + 2p$$ 6. **Divide both sides by 6:** $$y = \frac{\frac{64x^3}{125} + 2p}{6}$$ 7. **Simplify the expression:** $$y = \frac{64x^3}{125 \times 6} + \frac{2p}{6}$$ $$y = \frac{64x^3}{750} + \frac{p}{3}$$ **Final answer:** $$y = \frac{64x^3}{750} + \frac{p}{3}$$