Check Whether The Following Are Quadratic Equations (X−3)(2X+1)=X(X+5)

Given equation: (x − 3)(2x + 1) = x ( x + 5)

x (2x + 1) – 3 (2x + 1) = x ( x + 5)

=\( 2x^{2} + x – 6x – 3 = x^{2} + 5x \)

=\( 2x^{2} + x – 6x – 3 – x^{2} – 5x = 0\)

=\( 2x^{2} – x^{2} + x – 6x – 5x – 3 = 0\)

=\( x^{2} – 10x – 3 = 0 \)

The obtained equation \( x^{2} – 10x – 3 = 0 is in the form of ax^{2} + bx + c = 0 \)

where a = 1, b = -10 and c = -3

Therefore, the given equation (x − 3)(2x + 1) = x ( x + 5) is a quadratic equation

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