Solve \(4x^{2}+20x=0\) by extracting the full GCF. Apply the zero-product property to every factor, including the variable factor, and list all solutions.

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4x(x + 5) = 0 gives x = 4 or x = −5. The factor 4x equals zero when x = 0, not 4.

Factor out 4x: 4x(x + 5) = 0. Thus x = 0 or x = −5, and both values satisfy the original equation.

4(x² + 5x) = 0. The remaining shared factor x has not been factored, so the solutions are incomplete.

Dividing by x gives 4x + 20 = 0, so x = −5. This loses the solution x = 0.

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