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y2−15=2−y3\frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3}

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Factor sums and differences of cubesright chevron icon

Full solution

Q. y2−15=2−y3\frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3}
  1. Write Equation: Write down the original equation.\newliney2−15=2−y3\frac{y}{2} - \frac{1}{5} = 2 - \frac{y}{3}
  2. Find Common Denominator: Find a common denominator for the fractions to combine them effectively. The common denominator for 22, 55, and 33 is 3030.\newlineMultiply each term by 3030 to eliminate the denominators.\newline30(y/2)−30(1/5)=30(2)−30(y/3)30(y/2) - 30(1/5) = 30(2) - 30(y/3)
  3. Multiply by Common Denominator: Simplify each term. 15y−6=60−10y15y - 6 = 60 - 10y
  4. Simplify Terms: Move all yy terms to one side of the equation and constants to the other side.15y+10y=60+615y + 10y = 60 + 6
  5. Move Terms: Combine like terms.\newline25y=6625y = 66
  6. Combine Like Terms: Divide both sides by 2525 to solve for yy.\newliney=6625y = \frac{66}{25}
  7. Solve for y: Simplify the fraction if possible.\newliney=2.64y = 2.64

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