(3x + 12) (x + 4) = (4x^2 + 8x + 8x^2) / (2x) assuming that x is not 0
3x^2 +24x + 48 = (4x) ( x + 2 + 2x) / ( 2x)
3x^2 + 24x + 48 = 2 ( 3x + 2)
3x^2 + 24x + 48 = 6x + 4
3x^2 + 18x + 44 = 0
Using the Q formula
-18 ± √ (18^2 - 4 * 3 * 44) -18 ± √ ( -204) -18 ± 2√51 i
x = ______________________ = ____________ = ____________ = -3 ± √51 i / 3
2 * 3 6 6
Simplify the equation to: \(3(x+4)(x+4) = 2x(6x + 4) \div 2x\)
Note the 2x's on the right-hand side cancel out, so we have: \(6x+4 = 3(x+4)(x+4)\)
Now, expand the right-hand side: \(6x+4 = 3x^2 + 24x + 48\)
Convert into a quadratic: \(0 = 3x^2 + 18x + 44\)
Now, use the quadratic formula, and \(x = \color{brown}\boxed{{-3 \pm \sqrt {51} \over 3}}\)