(z^2+7)-5(4+z)=-19

Solution for (z^2+7)-5(4+z)=-19 equation:

Simplifying
(z2 + 7) + -5(4 + z) = -19

Reorder the terms:
(7 + z2) + -5(4 + z) = -19

Remove parenthesis around (7 + z2)
7 + z2 + -5(4 + z) = -19
7 + z2 + (4 * -5 + z * -5) = -19
7 + z2 + (-20 + -5z) = -19

Reorder the terms:
7 + -20 + -5z + z2 = -19

Combine like terms: 7 + -20 = -13
-13 + -5z + z2 = -19

Solving
-13 + -5z + z2 = -19

Solving for variable 'z'.

Reorder the terms:
-13 + 19 + -5z + z2 = -19 + 19

Combine like terms: -13 + 19 = 6
6 + -5z + z2 = -19 + 19

Combine like terms: -19 + 19 = 0
6 + -5z + z2 = 0

Factor a trinomial.
(2 + -1z)(3 + -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 '(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 = {2, 3}