$(x + 5) (x - 4) \cdot (4 + x) \cdot 0 = 0$

Answer

The equation has an infinite number of solutions.

Explanation

(x + 5) (x - 4) \cdot (4 + x) \cdot 0 (x^{2} - 4 x + 5 x - 20) \cdot (4 + x) \cdot 0 (x^{2} + x - 20) \cdot (4 + x) \cdot 0 (4 x^{2} + x^{3} + 4 x + x^{2} - 80 - 20 x) \cdot 0 (x^{3} + 5 x^{2} - 16 x - 80) \cdot 0 0 x^{3} + 0 x^{2} + 0 x + 0 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 simplify left side

Since the statement $0 = 0$ is TRUE for any value of $x$ , we conclude that the equation has infinitely many solutions.

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(x+5)(x−4)⋅(4+x)⋅0=0

The equation has an infinite number of solutions.

$(x + 5) (x - 4) \cdot (4 + x) \cdot 0 = 0$