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

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

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

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

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

Reorder the terms for easier multiplication:
2 * 3z(1 + z)(2 + z) = 3z(z + 3) + -1z + z

Multiply 2 * 3
6z(1 + z)(2 + z) = 3z(z + 3) + -1z + z

Multiply (1 + z) * (2 + z)
6z(1(2 + z) + z(2 + z)) = 3z(z + 3) + -1z + z
6z((2 * 1 + z * 1) + z(2 + z)) = 3z(z + 3) + -1z + z
6z((2 + 1z) + z(2 + z)) = 3z(z + 3) + -1z + z
6z(2 + 1z + (2 * z + z * z)) = 3z(z + 3) + -1z + z
6z(2 + 1z + (2z + z2)) = 3z(z + 3) + -1z + z

Combine like terms: 1z + 2z = 3z
6z(2 + 3z + z2) = 3z(z + 3) + -1z + z
(2 * 6z + 3z * 6z + z2 * 6z) = 3z(z + 3) + -1z + z
(12z + 18z2 + 6z3) = 3z(z + 3) + -1z + z

Reorder the terms:
12z + 18z2 + 6z3 = 3z(3 + z) + -1z + z
12z + 18z2 + 6z3 = (3 * 3z + z * 3z) + -1z + z
12z + 18z2 + 6z3 = (9z + 3z2) + -1z + z

Reorder the terms:
12z + 18z2 + 6z3 = 9z + -1z + z + 3z2

Combine like terms: 9z + -1z = 8z
12z + 18z2 + 6z3 = 8z + z + 3z2

Combine like terms: 8z + z = 9z
12z + 18z2 + 6z3 = 9z + 3z2

Solving
12z + 18z2 + 6z3 = 9z + 3z2

Solving for variable 'z'.

Reorder the terms:
12z + -9z + 18z2 + -3z2 + 6z3 = 9z + 3z2 + -9z + -3z2

Combine like terms: 12z + -9z = 3z
3z + 18z2 + -3z2 + 6z3 = 9z + 3z2 + -9z + -3z2

Combine like terms: 18z2 + -3z2 = 15z2
3z + 15z2 + 6z3 = 9z + 3z2 + -9z + -3z2

Reorder the terms:
3z + 15z2 + 6z3 = 9z + -9z + 3z2 + -3z2

Combine like terms: 9z + -9z = 0
3z + 15z2 + 6z3 = 0 + 3z2 + -3z2
3z + 15z2 + 6z3 = 3z2 + -3z2

Combine like terms: 3z2 + -3z2 = 0
3z + 15z2 + 6z3 = 0

Factor out the Greatest Common Factor (GCF), '3z'.
3z(1 + 5z + 2z2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(1 + 5z + 2z2)' equal to zero and attempt to solve:

Simplifying
1 + 5z + 2z2 = 0

Solving
1 + 5z + 2z2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
0.5 + 2.5z + z2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 2.5z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 2.5z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 2.5z + z2 = 0 + -0.5
2.5z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
2.5z + z2 = -0.5

The z term is 2.5z.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5z + 1.5625 + z2 = -0.5 + 1.5625

Reorder the terms:
1.5625 + 2.5z + z2 = -0.5 + 1.5625

Combine like terms: -0.5 + 1.5625 = 1.0625
1.5625 + 2.5z + z2 = 1.0625

Factor a perfect square on the left side:
(z + 1.25)(z + 1.25) = 1.0625

Calculate the square root of the right side: 1.030776406

Break this problem into two subproblems by setting 
(z + 1.25) equal to 1.030776406 and -1.030776406.

Subproblem 1
z + 1.25 = 1.030776406

Simplifying
z + 1.25 = 1.030776406

Reorder the terms:
1.25 + z = 1.030776406

Solving
1.25 + z = 1.030776406

Solving for variable 'z'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + z = 1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + z = 1.030776406 + -1.25
z = 1.030776406 + -1.25

Combine like terms: 1.030776406 + -1.25 = -0.219223594
z = -0.219223594

Simplifying
z = -0.219223594

Subproblem 2
z + 1.25 = -1.030776406

Simplifying
z + 1.25 = -1.030776406

Reorder the terms:
1.25 + z = -1.030776406

Solving
1.25 + z = -1.030776406

Solving for variable 'z'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + z = -1.030776406 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + z = -1.030776406 + -1.25
z = -1.030776406 + -1.25

Combine like terms: -1.030776406 + -1.25 = -2.280776406
z = -2.280776406

Simplifying
z = -2.280776406

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {-0.219223594, -2.280776406}
Solution
z = {0, -0.219223594, -2.280776406}