Question
$$2x(x-1)(x+6) = 2x(x-1)(x+6)$$
Answer
The equation has an infinite number of solutions.
Explanation
$$ \begin{aligned} 2x(x-1)(x+6) &= 2x(x-1)(x+6)&& \text{simplify left and right hand side} \\[1 em](2x^2-2x)(x+6) &= (2x^2-2x)(x+6)&& \\[1 em]2x^3+12x^2-2x^2-12x &= 2x^3+12x^2-2x^2-12x&& \\[1 em]2x^3+10x^2-12x &= 2x^3+10x^2-12x&& \text{move all terms to the left hand side } \\[1 em]2x^3+10x^2-12x-2x^3-10x^2+12x &= 0&& \text{simplify left side} \\[1 em]2x^3+10x^2-12x-2x^3-10x^2+12x &= 0&& \\[1 em]0 &= 0&& \\[1 em] \end{aligned} $$
Since the statement $ \color{blue}{ 0 = 0 } $ is TRUE for any value of $ x $, we conclude that the equation has infinitely many solutions.
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