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(a+3)x=(a+3)(a-2) equation

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Numerical solution:

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The solution

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(a + 3)*x = (a + 3)*(a - 2)
x(a+3)=(a−2)(a+3)x \left(a + 3\right) = \left(a - 2\right) \left(a + 3\right)
Simplify
Detail solution
Given the linear equation:
(a+3)*x = (a+3)*(a-2)

Expand brackets in the left part
a+3x = (a+3)*(a-2)

Expand brackets in the right part
a+3x = a+3a-2

Looking for similar summands in the left part:
x*(3 + a) = a+3a-2

Looking for similar summands in the right part:
x*(3 + a) = (-2 + a)*(3 + a)

Divide both parts of the equation by 3 + a
x = (-2 + a)*(3 + a) / (3 + a)

We get the answer: x = -2 + a
The solution of the parametric equation
Given the equation with a parameter:
x(a+3)=(a−2)(a+3)x \left(a + 3\right) = \left(a - 2\right) \left(a + 3\right)
Коэффициент при x равен
a+3a + 3
then possible cases for a :
a<−3a < -3
a=−3a = -3
Consider all cases in more detail:
With
a<−3a < -3
the equation
−x−6=0- x - 6 = 0
its solution
x=−6x = -6
With
a=−3a = -3
the equation
0=00 = 0
its solution
any x
The graph
Sum and product of roots [src] 
sum
-2 + I*im(a) + re(a)
re⁡(a)+iim⁡(a)−2\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} - 2 
=
-2 + I*im(a) + re(a)
re⁡(a)+iim⁡(a)−2\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} - 2 
product
-2 + I*im(a) + re(a)
re⁡(a)+iim⁡(a)−2\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} - 2 
=
-2 + I*im(a) + re(a)
re⁡(a)+iim⁡(a)−2\operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} - 2 
-2 + i*im(a) + re(a)
Rapid solution [src] 
x1 = -2 + I*im(a) + re(a)
x1=re⁡(a)+iim⁡(a)−2x_{1} = \operatorname{re}{\left(a\right)} + i \operatorname{im}{\left(a\right)} - 2 
x1 = re(a) + i*im(a) - 2
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