12z-1=z^2+35

Solution for 12z-1=z^2+35 equation:

Simplifying
12z + -1 = z2 + 35

Reorder the terms:
-1 + 12z = z2 + 35

Reorder the terms:
-1 + 12z = 35 + z2

Solving
-1 + 12z = 35 + z2

Solving for variable 'z'.

Reorder the terms:
-1 + -35 + 12z + -1z2 = 35 + z2 + -35 + -1z2

Combine like terms: -1 + -35 = -36
-36 + 12z + -1z2 = 35 + z2 + -35 + -1z2

Reorder the terms:
-36 + 12z + -1z2 = 35 + -35 + z2 + -1z2

Combine like terms: 35 + -35 = 0
-36 + 12z + -1z2 = 0 + z2 + -1z2
-36 + 12z + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
-36 + 12z + -1z2 = 0

Factor a trinomial.
(-6 + z)(6 + -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 '(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
Solution
z = {6, 6}