First, we apply distributive property as:
[tex]\begin{gathered} (x+1)(x+5)=x(x+10) \\ (x\cdot x)+(x\cdot5)+(1\cdot x)+(1\cdot5)=(x\cdot x)+(10\cdot x) \\ x^2+5x+x+5=x^2+10x \end{gathered}[/tex]Then, adding like terms:
[tex]x^2+6x+5=x^2+10x[/tex]Subtracting x² from both sides:
[tex]\begin{gathered} x^2+6x+5-x^2=x^2+10x-x^2 \\ 6x+5=10x \end{gathered}[/tex]Subtracting 6x from both sides:
[tex]\begin{gathered} 6x+5-6x=10x-6x \\ 5=4x \end{gathered}[/tex]Finally, dividing by 4:
[tex]\begin{gathered} \frac{5}{4}=\frac{4x}{4} \\ 1.25=x \end{gathered}[/tex]Answer: x
