8-7z=z^2+20

Solution for 8-7z=z^2+20 equation:

Simplifying
8 + -7z = z2 + 20

Reorder the terms:
8 + -7z = 20 + z2

Solving
8 + -7z = 20 + z2

Solving for variable 'z'.

Reorder the terms:
8 + -20 + -7z + -1z2 = 20 + z2 + -20 + -1z2

Combine like terms: 8 + -20 = -12
-12 + -7z + -1z2 = 20 + z2 + -20 + -1z2

Reorder the terms:
-12 + -7z + -1z2 = 20 + -20 + z2 + -1z2

Combine like terms: 20 + -20 = 0
-12 + -7z + -1z2 = 0 + z2 + -1z2
-12 + -7z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-12 + -7z + -1z2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12 + 7z + z2) = 0

Factor a trinomial.
-1((4 + z)(3 + z)) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(4 + z)' equal to zero and attempt to solve:

Simplifying
4 + z = 0

Solving
4 + z = 0

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

Add '-4' to each side of the equation.
4 + -4 + z = 0 + -4

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

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

Simplifying
z = -4
Subproblem 2
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
Solution
z = {-4, -3}