z^2+5Z+2z=0

Solution for z^2+5Z+2z=0 equation:

Simplifying
z2 + 5Z + 2z = 0

Reorder the terms:
5Z + 2z + z2 = 0

Solving
5Z + 2z + z2 = 0

Solving for variable 'Z'.

Move all terms containing Z to the left, all other terms to the right.

Add '-2z' to each side of the equation.
5Z + 2z + -2z + z2 = 0 + -2z

Combine like terms: 2z + -2z = 0
5Z + 0 + z2 = 0 + -2z
5Z + z2 = 0 + -2z
Remove the zero:
5Z + z2 = -2z

Add '-1z2' to each side of the equation.
5Z + z2 + -1z2 = -2z + -1z2

Combine like terms: z2 + -1z2 = 0
5Z + 0 = -2z + -1z2
5Z = -2z + -1z2

Divide each side by '5'.
Z = -0.4z + -0.2z2

Simplifying
Z = -0.4z + -0.2z2