z^2+2z+6+3z=0

Solution for z^2+2z+6+3z=0 equation:

Simplifying
z2 + 2z + 6 + 3z = 0

Reorder the terms:
6 + 2z + 3z + z2 = 0

Combine like terms: 2z + 3z = 5z
6 + 5z + z2 = 0

Solving
6 + 5z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
2 + z = 0

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

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

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

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