Question
$$(x+1)(x+3)(x+5)(x+7)+9 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x+1)(x+3)(x+5)(x+7)+9 &= 0&& \text{simplify left side} \\[1 em](x^2+3x+x+3)(x+5)(x+7)+9 &= 0&& \\[1 em](x^2+4x+3)(x+5)(x+7)+9 &= 0&& \\[1 em](x^3+5x^2+4x^2+20x+3x+15)(x+7)+9 &= 0&& \\[1 em](x^3+9x^2+23x+15)(x+7)+9 &= 0&& \\[1 em]x^4+16x^3+86x^2+176x+105+9 &= 0&& \\[1 em]x^4+16x^3+86x^2+176x+114 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Equations Solver