Check whether the following is a quadratic equation:
$(x-3)(2x+1) = x(x+5)$
$(x-3)(2x+1) = x(x+5)$
(A) Expand the left side: $(x-3)(2x+1) = 2x^2 + x - 6x - 3 = 2x^2 - 5x - 3$.
Expand the right side: $x(x+5) = x^2 + 5x$.
Equating both sides: $2x^2 - 5x - 3 = x^2 + 5x$.
Rearranging the terms to one side: $2x^2 - x^2 - 5x - 5x - 3 = 0$.
Simplifying the expression: $x^2 - 10x - 3 = 0$.
Since this equation is in the form $ax^2 + bx + c = 0$ where $a \neq 0$,it is a quadratic equation.
Expand the right side: $x(x+5) = x^2 + 5x$.
Equating both sides: $2x^2 - 5x - 3 = x^2 + 5x$.
Rearranging the terms to one side: $2x^2 - x^2 - 5x - 5x - 3 = 0$.
Simplifying the expression: $x^2 - 10x - 3 = 0$.
Since this equation is in the form $ax^2 + bx + c = 0$ where $a \neq 0$,it is a quadratic equation.
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