Question
$$(3+x)\cdot(5+x)\cdot(11+x) = 300$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (3+x)\cdot(5+x)\cdot(11+x) &= 300&& \text{simplify left side} \\[1 em](15+3x+5x+x^2)\cdot(11+x) &= 300&& \\[1 em](x^2+8x+15)\cdot(11+x) &= 300&& \\[1 em]11x^2+x^3+88x+8x^2+165+15x &= 300&& \\[1 em]x^3+19x^2+103x+165 &= 300&& \text{move all terms to the left hand side } \\[1 em]x^3+19x^2+103x+165-300 &= 0&& \text{simplify left side} \\[1 em]x^3+19x^2+103x-135 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver