Answer:
[tex]x=-1,\:x=-6[/tex]
Step-by-step explanation:
We can solve this question by applying a quadratic equation, but it would be easier to simply factor the equation. In other words, let's begin by factoring the expression [tex]x^2[/tex] + 7x + 6,
Break this expression down into groups - [tex]\left(x^2+x\right)+\left(6x+6\right)[/tex],
Factor out x from " [tex]\left(x^2+x\right)[/tex] " = [tex]{\quad }x\left(x+1\right)[/tex],
Respectively factor out 6 from " [tex]6x+6\mathrm{}[/tex] " = [tex]6\left(x+1\right)[/tex],
[tex]x\left(x+1\right)+6\left(x+1\right)[/tex] - and now we can group like terms - [tex]\left(x+1\right)\left(x+6\right)[/tex]
Since we have factored this expression, let's make it equivalent to 0, and solve for x. By the Zero Factor Principle we should receive two solutions,
[tex]\left(x+1\right)\left(x+6\right)=0[/tex],
[tex]x+1=0: x=-1[/tex] / [tex]x+6=0: x=-6[/tex],
The solutions to this equation should thus be : [tex]x=-1,\:x=-6[/tex]
