Question
$$(x\cdot3-3x\cdot2+8x-24)(x+2)x\cdot2-x-6 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x\cdot3-3x\cdot2+8x-24)(x+2)x\cdot2-x-6 &= 0&& \text{simplify left side} \\[1 em](3x-6x+8x-24)(x+2)x\cdot2-x-6 &= 0&& \\[1 em](5x-24)(x+2)x\cdot2-x-6 &= 0&& \\[1 em](5x^2+10x-24x-48)x\cdot2-x-6 &= 0&& \\[1 em](5x^2-14x-48)x\cdot2-x-6 &= 0&& \\[1 em](5x^3-14x^2-48x)\cdot2-x-6 &= 0&& \\[1 em]10x^3-28x^2-96x-x-6 &= 0&& \\[1 em]10x^3-28x^2-97x-6 &= 0&& \\[1 em] \end{aligned} $$
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