Solving $|a+1|+|2a+5|=5$ How to solve this equation?

$$|a+1|+|2a+5|=5$$

Here is my solution but it seems that my answers are wrong.

$$|a+1|+|2a+5|=5$$

Case 1:

$$a+1+2a+5=5$$

$$a = \frac{1}{3}$$

Case 2:

$$a+1-2a-5=5$$

$$a=-11$$
HINT: There are three cases for solving $|a+1|+|2a+5|=5$, as follows

Case 1: $a&lt; -\frac52$
$$-(a+1)-(2a+5)=5$$
Case 2: $-\frac52\le a\le -1$
$$-(a+1)+(2a+5)=5$$
Case 3: $a&gt; -1$
$$(a+1)+(2a+5)=5$$
You can find feasible values of $a$ in above three cases.
Squaring both sides gives

$$(a+1)^2+|(a+1)(2a+5)|+(2a+5)^2=5^2,$$

or

$$|(a+1)(2a+5)|=25-(a^2+2a+1)-(4a^2+20a+25),$$

which gives

$$|(a+1)(2a+5)|=-5a^2-22a-1.$$

Squaring again, we obtain

$$(a+1)^2(2a+5)^2=(5a^2+22a+1)^2,$$

or

$$(2a^2+7a+5)^2=(5a^2+22a+1)^2,$$

or

$$(2a^2+7a+5)^2-(5a^2+22a+1)^2=0.$$

Factorising then gives

$$(-3a^2-15a+4)(7a^2+29a+6)=0,$$ from which you should be able to proceed.