2z(z+1)+3(z+2)=3z(z+2)

Solution for 2z(z+1)+3(z+2)=3z(z+2) equation:

Simplifying
2z(z + 1) + 3(z + 2) = 3z(z + 2)

Reorder the terms:
2z(1 + z) + 3(z + 2) = 3z(z + 2)
(1 * 2z + z * 2z) + 3(z + 2) = 3z(z + 2)
(2z + 2z2) + 3(z + 2) = 3z(z + 2)

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

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

Combine like terms: 2z + 3z = 5z
6 + 5z + 2z2 = 3z(z + 2)

Reorder the terms:
6 + 5z + 2z2 = 3z(2 + z)
6 + 5z + 2z2 = (2 * 3z + z * 3z)
6 + 5z + 2z2 = (6z + 3z2)

Solving
6 + 5z + 2z2 = 6z + 3z2

Solving for variable 'z'.

Reorder the terms:
6 + 5z + -6z + 2z2 + -3z2 = 6z + 3z2 + -6z + -3z2

Combine like terms: 5z + -6z = -1z
6 + -1z + 2z2 + -3z2 = 6z + 3z2 + -6z + -3z2

Combine like terms: 2z2 + -3z2 = -1z2
6 + -1z + -1z2 = 6z + 3z2 + -6z + -3z2

Reorder the terms:
6 + -1z + -1z2 = 6z + -6z + 3z2 + -3z2

Combine like terms: 6z + -6z = 0
6 + -1z + -1z2 = 0 + 3z2 + -3z2
6 + -1z + -1z2 = 3z2 + -3z2

Combine like terms: 3z2 + -3z2 = 0
6 + -1z + -1z2 = 0

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

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

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

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

Divide each side by '-1'.
z = 2

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

Simplifying
3 + z = 0

Solving
3 + z = 0

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

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

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

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

Simplifying
z = -3
Solution
z = {2, -3}