12z=z^2+35

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

Simplifying
12z = z2 + 35

Reorder the terms:
12z = 35 + z2

Solving
12z = 35 + z2

Solving for variable 'z'.

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

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

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

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

Factor a trinomial.
(-7 + z)(5 + -1z) = 0

Subproblem 1
Set the factor '(-7 + z)' equal to zero and attempt to solve:

Simplifying
-7 + z = 0

Solving
-7 + z = 0

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

Add '7' to each side of the equation.
-7 + 7 + z = 0 + 7

Combine like terms: -7 + 7 = 0
0 + z = 0 + 7
z = 0 + 7

Combine like terms: 0 + 7 = 7
z = 7

Simplifying
z = 7
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 = {7, 5}