z(3z+2)=(z+2)

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

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

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

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

Remove parenthesis around (2 + z)
2z + 3z2 = 2 + z

Solving
2z + 3z2 = 2 + z

Solving for variable 'z'.

Reorder the terms:
-2 + 2z + -1z + 3z2 = 2 + z + -2 + -1z

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

Reorder the terms:
-2 + 1z + 3z2 = 2 + -2 + z + -1z

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

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

Factor a trinomial.
(-1 + -1z)(2 + -3z) = 0

Subproblem 1
Set the factor '(-1 + -1z)' equal to zero and attempt to solve:

Simplifying
-1 + -1z = 0

Solving
-1 + -1z = 0

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

Add '1' to each side of the equation.
-1 + 1 + -1z = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1z = 0 + 1
-1z = 0 + 1

Combine like terms: 0 + 1 = 1
-1z = 1

Divide each side by '-1'.
z = -1

Simplifying
z = -1
Subproblem 2
Set the factor '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

Solving
2 + -3z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3z = 0 + -2

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

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

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {-1, 0.6666666667}