z^2+35=12z+35

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

Simplifying
z2 + 35 = 12z + 35

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

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

Add '-35' to each side of the equation.
35 + -35 + z2 = 35 + -35 + 12z

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

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

Solving
z2 = 12z

Solving for variable 'z'.

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

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

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

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
Set the factor '(-12 + z)' equal to zero and attempt to solve:

Simplifying
-12 + z = 0

Solving
-12 + z = 0

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

Add '12' to each side of the equation.
-12 + 12 + z = 0 + 12

Combine like terms: -12 + 12 = 0
0 + z = 0 + 12
z = 0 + 12

Combine like terms: 0 + 12 = 12
z = 12

Simplifying
z = 12
Solution
z = {0, 12}