z(z+3)=-2

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

Simplifying
z(z + 3) = -2

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

Solving
3z + z2 = -2

Solving for variable 'z'.

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

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

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

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

Simplifying
1 + z = 0

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

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

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

Simplifying
z = -1
Solution
z = {-2, -1}