Let X = (2A +3)

So,

5sinX +3cosX = 0

5sinX = -3cosX

sinX /cosX = -3/5

tanX = -3/5 ----------negative tan value, so X is in the 2nd or 4th quadrants

X = arctan(-3/5) = -0.5404195 radian

In the 2nd quadrant,

X = pi -0.5404195 = 2.6012 rad

2A +3 = 2.6012

A = (2.6012 -3) /2 = -0.1994 rad less than 0, so not counted.

In the 4th quadrant,

X = 2pi -0.5404195 = 5.7428 rad

2A +3 = 5.7428

A = (5.7428 -3) /2 = 1.3714 rad -------one counted.

Now, the period of the tangent function is pi.

Meaning, for every pi radians, the X here will repeat having tangent value of -0.5404195.

So, in the 2nd quadrant, after one revolution,

X = 3pi -0.5404195 = 8.8844 rad

A = (8.8844 -3) /2 = 2.9422 rad ------two counted.

In the next 4th quadrant,

X = 4pi -0.5404195 = 12.0260

A = (12.0260 -3)/2 = 4.513 rad --------3 counted.

In the next 2nd quadrant again,

X = 5pi -0.5404195 = 15.1675 rad

A = (15.1675 -3) /2 = 6.0838 rad ------more than 5.0, so not counted anymore.

Therefore, A = 1.3714, 2.9422 and 4.513 radians. ----------answer.