z^2+4z=-3

Solution for z^2+4z=-3 equation:

Simplifying
z2 + 4z = -3

Reorder the terms:
4z + z2 = -3

Solving
4z + z2 = -3

Solving for variable 'z'.

Reorder the terms:
3 + 4z + z2 = -3 + 3

Combine like terms: -3 + 3 = 0
3 + 4z + z2 = 0

Factor a trinomial.
(3 + z)(1 + 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 '(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 = {-3, -1}