Help with implicit differentiation!!?

Find dy/dx by using implicit differentiation.

(2x+3y)^2=x^2+y^2

I know the answer is -(3x+2y)/2(3x+4y) but I am not sure how they got that.

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    (2x + 3y)^2 = x^2 + y^2

    2 * (2x + 3y) * (2 * dx + 3 * dy) = 2x * dx + 2y * dy

    (2x + 3y) * (2 * dx + 3 * dy) = x * dx + y * dy

    (4x + 6y) * dx + (6x + 9y) * dy = x * dx + y * dy

    (4x + 6y) * dx - x * dx = y * dy - (6x + 9y) * dy

    (4x - x + 6y) * dx = (y - 6x - 9y) * dy

    (3x + 6y) * dx = (-8y - 6x) * dy

    3 * (x + 2y) * dx = -2 * (4y + 3x) * dy

    dy/dx = -3 * (x + 2y) / (2 * (4y + 3x))

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