Solve \( 6 x(x+2)=-42 \) by completing the square \( x=\square \)

Solve the equation \( 6x(x+2)=-42 \). Solve the equation(The complex numbers system) by following steps: - step0: Solve using the quadratic formula in the complex numbers system: \(6x\left(x+2\right)=-42\) - step1: Expand the expression: \(6x^{2}+12x=-42\) - step2: Move the expression to the left side: \(6x^{2}+12x+42=0\) - step3: Solve using the quadratic formula: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 6\times 42}}{2\times 6}\) - step4: Simplify the expression: \(x=\frac{-12\pm \sqrt{12^{2}-4\times 6\times 42}}{12}\) - step5: Simplify the expression: \(x=\frac{-12\pm \sqrt{-864}}{12}\) - step6: Simplify the expression: \(x=\frac{-12\pm 12\sqrt{6}\times i}{12}\) - step7: Separate into possible cases: \(\begin{align}&x=\frac{-12+12\sqrt{6}\times i}{12}\\&x=\frac{-12-12\sqrt{6}\times i}{12}\end{align}\) - step8: Simplify the expression: \(\begin{align}&x=-1+\sqrt{6}\times i\\&x=\frac{-12-12\sqrt{6}\times i}{12}\end{align}\) - step9: Simplify the expression: \(\begin{align}&x=-1+\sqrt{6}\times i\\&x=-1-\sqrt{6}\times i\end{align}\) - step10: Rewrite: \(x_{1}=-1-\sqrt{6}\times i,x_{2}=-1+\sqrt{6}\times i\) - step11: Remove the complex number(s): \(\textrm{No real solution}\) The equation \(6x(x+2)=-42\) does not have any real solutions. Therefore, there is no value of \(x\) that satisfies the equation.