z(z-6)+2z=3+z(z-2)

Solution for z(z-6)+2z=3+z(z-2) equation:

Simplifying
z(z + -6) + 2z = 3 + z(z + -2)

Reorder the terms:
z(-6 + z) + 2z = 3 + z(z + -2)
(-6 * z + z * z) + 2z = 3 + z(z + -2)
(-6z + z2) + 2z = 3 + z(z + -2)

Reorder the terms:
-6z + 2z + z2 = 3 + z(z + -2)

Combine like terms: -6z + 2z = -4z
-4z + z2 = 3 + z(z + -2)

Reorder the terms:
-4z + z2 = 3 + z(-2 + z)
-4z + z2 = 3 + (-2 * z + z * z)
-4z + z2 = 3 + (-2z + z2)

Add '-1z2' to each side of the equation.
-4z + z2 + -1z2 = 3 + -2z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-4z + 0 = 3 + -2z + z2 + -1z2
-4z = 3 + -2z + z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-4z = 3 + -2z + 0
-4z = 3 + -2z

Solving
-4z = 3 + -2z

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.
-4z + 2z = 3 + -2z + 2z

Combine like terms: -4z + 2z = -2z
-2z = 3 + -2z + 2z

Combine like terms: -2z + 2z = 0
-2z = 3 + 0
-2z = 3

Divide each side by '-2'.
z = -1.5

Simplifying
z = -1.5