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anemone
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MHB
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Find all real solution(s) for the equation $(x^2+2x+3)(x^2+x+1)(5x+3)=1001$.
The equation we are trying to solve is $(x^2+2x+3)(x^2+x+1)(5x+3)=1001$.
Real solutions are values of x that make the equation true when substituted into the equation.
To solve this equation, we can use the quadratic formula to find the solutions for the quadratic terms, and then use algebraic manipulation to solve for the remaining linear term.
Yes, there are restrictions on the solutions. Since the equation contains a quadratic term, the solutions must be real numbers. Additionally, the solutions must also make the equation true when substituted into the equation.
This equation has four solutions, as it is a quartic equation. However, some solutions may be repeated or complex numbers.