z^2+4z=21+z-3

Solution for z^2+4z=21+z-3 equation:

Simplifying
z2 + 4z = 21 + z + -3

Reorder the terms:
4z + z2 = 21 + z + -3

Reorder the terms:
4z + z2 = 21 + -3 + z

Combine like terms: 21 + -3 = 18
4z + z2 = 18 + z

Solving
4z + z2 = 18 + z

Solving for variable 'z'.

Reorder the terms:
-18 + 4z + -1z + z2 = 18 + z + -18 + -1z

Combine like terms: 4z + -1z = 3z
-18 + 3z + z2 = 18 + z + -18 + -1z

Reorder the terms:
-18 + 3z + z2 = 18 + -18 + z + -1z

Combine like terms: 18 + -18 = 0
-18 + 3z + z2 = 0 + z + -1z
-18 + 3z + z2 = z + -1z

Combine like terms: z + -1z = 0
-18 + 3z + z2 = 0

Factor a trinomial.
(-6 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1z = 0 + 6

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

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

Divide each side by '-1'.
z = -6

Simplifying
z = -6
Subproblem 2
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

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

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

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Solution
z = {-6, 3}