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# Equation

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Solve for x: (3x + 12)(x + 4) = (4x^2 + 8x + 8x^2)/(2x).

Nov 13, 2022

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I'm assuming you're solving $$(3x+12)(x+4) = \frac{4x^2+8x+8x^2}{2x}$$. With this, start by simplifying the RHS (right hand side) to $$2x+4+4x$$, which is equal to $$6x+4$$

Now, expand the LHS (left hand side) to get that $$3x^2+24x+48 = 6x+4$$. Shift the stuff on the RHS to the LHS to get $$3x^2+18x+42=0$$. Using the quadratic equation, the answers are $$x=-3 + \sqrt{5}i$$ and $$x = -3-\sqrt{5}i$$ (complex roots).

Hope this helped

Nov 13, 2022