z^2=7z-12

Solution for z^2=7z-12 equation:

Simplifying
z2 = 7z + -12

Reorder the terms:
z2 = -12 + 7z

Solving
z2 = -12 + 7z

Solving for variable 'z'.

Reorder the terms:
12 + -7z + z2 = -12 + 7z + 12 + -7z

Reorder the terms:
12 + -7z + z2 = -12 + 12 + 7z + -7z

Combine like terms: -12 + 12 = 0
12 + -7z + z2 = 0 + 7z + -7z
12 + -7z + z2 = 7z + -7z

Combine like terms: 7z + -7z = 0
12 + -7z + z2 = 0

Factor a trinomial.
(3 + -1z)(4 + -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 '(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
Solution
z = {3, 4}