text: # (x+3)(x-2)=(x-1)(x+1)
  
  ## Simple and best practice solution for (x+3)(x-2)=(x-1)(x+1) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
  
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  ## Solution for (x+3)(x-2)=(x-1)(x+1) equation:
  
  (x+3)(x-2)=(x-1)(x+1)
  We move all terms to the left:
  (x+3)(x-2)-((x-1)(x+1))=0
  We use the square of the difference formula
  x^2+(x+3)(x-2)+1=0
  We multiply parentheses ..
  x^2+(+x^2-2x+3x-6)+1=0
  We get rid of parentheses
  x^2+x^2-2x+3x-6+1=0
  We add all the numbers together, and all the variables
  2x^2+x-5=0
  a = 2; b = 1; c = -5;Δ = b2-4acΔ = 12-4·2·(-5)Δ = 41The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{41}}{2*2}=\frac{-1-\sqrt{41}}{4}$
  $x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*2}=\frac{-1+\sqrt{41}}{4}$
  
  `
explanation: The document contains a math equation and a detailed solution to the equation. It provides step-by-step instructions on how to solve the equation \((x+3)(x-2)=(x-1)(x+1)\), including the use of the quadratic formula to find the roots.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # (x+3)(x-2)=(x-1)(x+1)
  
  ## Simple and best practice solution for (x+3)(x-2)=(x-1)(x+1) equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.
  
  If it's not what You are looking for type in the equation solver your own equation and let us solve it.
  
  ## Solution for (x+3)(x-2)=(x-1)(x+1) equation:
  
  (x+3)(x-2)=(x-1)(x+1)
  We move all terms to the left:
  (x+3)(x-2)-((x-1)(x+1))=0
  We use the square of the difference formula
  x^2+(x+3)(x-2)+1=0
  We multiply parentheses ..
  x^2+(+x^2-2x+3x-6)+1=0
  We get rid of parentheses
  x^2+x^2-2x+3x-6+1=0
  We add all the numbers together, and all the variables
  2x^2+x-5=0
  a = 2; b = 1; c = -5;Δ = b2-4acΔ = 12-4·2·(-5)Δ = 41The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{41}}{2*2}=\frac{-1-\sqrt{41}}{4}$
  $x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{41}}{2*2}=\frac{-1+\sqrt{41}}{4}$
  
  `
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math equation and a detailed solution to the equation. It provides step-by-step instructions on how to solve the equation \((x+3)(x-2)=(x-1)(x+1)\), including the use of the quadratic formula to find the roots.
  
  Label: question-and-answer