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5x-3y=6z equation

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Numerical solution:

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The solution

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5*x - 3*y = 6*z
5x−3y=6z5 x - 3 y = 6 z
Simplify
Detail solution
Given the linear equation:
5*x-3*y = 6*z

Looking for similar summands in the left part:
-3*y + 5*x = 6*z

Move the summands with the other variables
from left part to right part, we given:
5x=3y+6z5 x = 3 y + 6 z
Divide both parts of the equation by 5
x = 3*y + 6*z / (5)

We get the answer: x = 3*y/5 + 6*z/5
The graph
Rapid solution [src] 
     3*re(y)   6*re(z)     /3*im(y)   6*im(z)\
x1 = ------- + ------- + I*|------- + -------|
        5         5        \   5         5   /
x1=i(3im⁡(y)5+6im⁡(z)5)+3re⁡(y)5+6re⁡(z)5x_{1} = i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5} 
x1 = i*(3*im(y)/5 + 6*im(z)/5) + 3*re(y)/5 + 6*re(z)/5
Sum and product of roots [src] 
sum
3*re(y)   6*re(z)     /3*im(y)   6*im(z)\
------- + ------- + I*|------- + -------|
   5         5        \   5         5   /
i(3im⁡(y)5+6im⁡(z)5)+3re⁡(y)5+6re⁡(z)5i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5} 
=
3*re(y)   6*re(z)     /3*im(y)   6*im(z)\
------- + ------- + I*|------- + -------|
   5         5        \   5         5   /
i(3im⁡(y)5+6im⁡(z)5)+3re⁡(y)5+6re⁡(z)5i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5} 
product
3*re(y)   6*re(z)     /3*im(y)   6*im(z)\
------- + ------- + I*|------- + -------|
   5         5        \   5         5   /
i(3im⁡(y)5+6im⁡(z)5)+3re⁡(y)5+6re⁡(z)5i \left(\frac{3 \operatorname{im}{\left(y\right)}}{5} + \frac{6 \operatorname{im}{\left(z\right)}}{5}\right) + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5} 
=
3*re(y)   6*re(z)   3*I*(2*im(z) + im(y))
------- + ------- + ---------------------
   5         5                5
3i(im⁡(y)+2im⁡(z))5+3re⁡(y)5+6re⁡(z)5\frac{3 i \left(\operatorname{im}{\left(y\right)} + 2 \operatorname{im}{\left(z\right)}\right)}{5} + \frac{3 \operatorname{re}{\left(y\right)}}{5} + \frac{6 \operatorname{re}{\left(z\right)}}{5} 
3*re(y)/5 + 6*re(z)/5 + 3*i*(2*im(z) + im(y))/5
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