z(z+1)=12

Solution for z(z+1)=12 equation:

Simplifying
z(z + 1) = 12

Reorder the terms:
z(1 + z) = 12
(1 * z + z * z) = 12
(1z + z2) = 12

Solving
1z + z2 = 12

Solving for variable 'z'.

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

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

Factor a trinomial.
(-4 + -1z)(3 + -1z) = 0

Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
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
Solution
z = {-4, 3}