(z^2+4)-7(3+z)=-27

Solution for (z^2+4)-7(3+z)=-27 equation:

Simplifying
(z2 + 4) + -7(3 + z) = -27

Reorder the terms:
(4 + z2) + -7(3 + z) = -27

Remove parenthesis around (4 + z2)
4 + z2 + -7(3 + z) = -27
4 + z2 + (3 * -7 + z * -7) = -27
4 + z2 + (-21 + -7z) = -27

Reorder the terms:
4 + -21 + -7z + z2 = -27

Combine like terms: 4 + -21 = -17
-17 + -7z + z2 = -27

Solving
-17 + -7z + z2 = -27

Solving for variable 'z'.

Reorder the terms:
-17 + 27 + -7z + z2 = -27 + 27

Combine like terms: -17 + 27 = 10
10 + -7z + z2 = -27 + 27

Combine like terms: -27 + 27 = 0
10 + -7z + z2 = 0

Factor a trinomial.
(2 + -1z)(5 + -1z) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

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

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {2, 5}