7z-z^2=6

Solution for 7z-z^2=6 equation:

Simplifying
7z + -1z2 = 6

Solving
7z + -1z2 = 6

Solving for variable 'z'.

Reorder the terms:
-6 + 7z + -1z2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 7z + -1z2 = 0

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

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

Simplifying
-6 + z = 0

Solving
-6 + z = 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 + z = 0 + 6

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

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

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

Simplifying
1 + -1z = 0

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

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

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

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

Simplifying
z = 1
Solution
z = {6, 1}