Solve the System of Equations x^3+6x^2+11x+6=0 , x=-3

$x^{3} + 6 x^{2} + 11 x + 6 = 0$ , $x = - 3$

Replace all occurrences of $x$ with $- 3$ in each equation.

Replace all occurrences of $x$ in $x^{3} + 6 x^{2} + 11 x + 6 = 0$ with $- 3$ .

${(- 3)}^{3} + 6 {(- 3)}^{2} + 11 (- 3) + 6 = 0$

$x = - 3$

Simplify the left side.

Simplify ${(- 3)}^{3} + 6 {(- 3)}^{2} + 11 (- 3) + 6$ .

Simplify each term.

Raise $- 3$ to the power of $3$ .

$- 27 + 6 {(- 3)}^{2} + 11 (- 3) + 6 = 0$

$x = - 3$

Raise $- 3$ to the power of $2$ .

$- 27 + 6 \cdot 9 + 11 (- 3) + 6 = 0$

$x = - 3$

Multiply $6$ by $9$ .

$- 27 + 54 + 11 (- 3) + 6 = 0$

$x = - 3$

Multiply $11$ by $- 3$ .

$- 27 + 54 - 33 + 6 = 0$

$x = - 3$

$- 27 + 54 - 33 + 6 = 0$

$x = - 3$

Simplify by adding and subtracting.

Add $- 27$ and $54$ .

$27 - 33 + 6 = 0$

$x = - 3$

Subtract $33$ from $27$ .

$- 6 + 6 = 0$

$x = - 3$

Add $- 6$ and $6$ .

$0 = 0$

$x = - 3$

$0 = 0$

$x = - 3$

$0 = 0$

$x = - 3$

$0 = 0$

$x = - 3$

$0 = 0$

$x = - 3$

Remove any equations from the system that are always true.

$x = - 3$