z(z-12)=-27

Solution for z(z-12)=-27 equation:

Simplifying
z(z + -12) = -27

Reorder the terms:
z(-12 + z) = -27
(-12 * z + z * z) = -27
(-12z + z2) = -27

Solving
-12z + z2 = -27

Solving for variable 'z'.

Reorder the terms:
27 + -12z + z2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + -12z + z2 = 0

Factor a trinomial.
(3 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 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 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {3, 9}