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Find the value of aa.\newline(15n+an2)(7n4n2+9)=12n212n10\qquad(-1-5n+an^2)-(7n-4n^2+9)=12n^2-12n-10

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Q. Find the value of aa.\newline(15n+an2)(7n4n2+9)=12n212n10\qquad(-1-5n+an^2)-(7n-4n^2+9)=12n^2-12n-10
  1. Simplify Left Side: Step Title: Simplify the Left Side of the Equation\newlineConcise Step Description: Combine like terms on the left side of the equation.\newlineStep Calculation: (15n+an2)(7n4n2+9)=15n+an27n+4n29(-1 - 5n + an^2) - (7n - 4n^2 + 9) = -1 - 5n + an^2 - 7n + 4n^2 - 9\newlineStep Output: Simplified Left Side: an212n+(4n2)10an^2 - 12n + (4n^2) - 10
  2. Simplify Right Side: Step Title: Simplify the Right Side of the Equation\newlineConcise Step Description: The right side of the equation is already simplified.\newlineStep Calculation: No calculation needed.\newlineStep Output: Simplified Right Side: 12n212n1012n^2 - 12n - 10
  3. Set Equal: Step Title: Set the Left Side Equal to the Right Side\newlineConcise Step Description: Set the simplified left side of the equation equal to the simplified right side.\newlineStep Calculation: an212n+4n210=12n212n10a n^2 - 12n + 4n^2 - 10 = 12n^2 - 12n - 10\newlineStep Output: Equation Set: an2+4n212n10=12n212n10a n^2 + 4n^2 - 12n - 10 = 12n^2 - 12n - 10
  4. Combine Like Terms: Step Title: Combine Like Terms on Both Sides\newlineConcise Step Description: Combine like terms on both sides to isolate the variable aa.\newlineStep Calculation: an2+4n2=12n2a n^2 + 4n^2 = 12n^2 and 12n=12n-12n = -12n and 10=10-10 = -10\newlineStep Output: Combined Like Terms: an2+4n2=12n2a n^2 + 4n^2 = 12n^2
  5. Solve for a: Step Title: Solve for a\newlineConcise Step Description: Isolate the variable aa by subtracting 4n24n^2 from both sides of the equation.\newlineStep Calculation: an2+4n24n2=12n24n2an^2 + 4n^2 - 4n^2 = 12n^2 - 4n^2\newlineStep Output: Isolated Variable: an2=8n2an^2 = 8n^2
  6. Divide by n2n^2: Step Title: Divide by n2n^2\newlineConcise Step Description: Divide both sides of the equation by n2n^2 to solve for aa.\newlineStep Calculation: an2n2=8n2n2\frac{an^2}{n^2} = \frac{8n^2}{n^2}\newlineStep Output: Solved for aa: a=8a = 8