[tex]\displaystyle\\
x^3+7x^2+13x+4=0\\\\
x^3+\underbrace{4x^2+3x^2}_{7x^2}+\underbrace{12x+x}_{13x}+4=0\\\\
(x^3+4x^2) + (3x^2 + 12x)+(x+4)=0\\\\
x^2(x+4)+3x(x+4)+(x+4)=0\\\\
(x+4)(x^2 + 3x +1)=0\\\\
x+4 = 0~~~\Longrightarrow~~~\boxed{x_1 = -4}\\\\
x^2 + 3x +1=0\\\\
x_{23}= \frac{-b\pm \sqrt{b^2-4ac} }{2a}= \frac{-3\pm \sqrt{3^2-4\cdot 1 \cdot 1} }{2\cdot 1}= \frac{-3\pm \sqrt{5} }{2}\\\\
\boxed{x_2 = \frac{-3-\sqrt{5} }{2}}\\\\
\boxed{x_3 = \frac{-3+\sqrt{5} }{2}}[/tex]
