z^2-2z=6-3z

Solution for z^2-2z=6-3z equation:

Simplifying
z2 + -2z = 6 + -3z

Reorder the terms:
-2z + z2 = 6 + -3z

Solving
-2z + z2 = 6 + -3z

Solving for variable 'z'.

Reorder the terms:
-6 + -2z + 3z + z2 = 6 + -3z + -6 + 3z

Combine like terms: -2z + 3z = 1z
-6 + 1z + z2 = 6 + -3z + -6 + 3z

Reorder the terms:
-6 + 1z + z2 = 6 + -6 + -3z + 3z

Combine like terms: 6 + -6 = 0
-6 + 1z + z2 = 0 + -3z + 3z
-6 + 1z + z2 = -3z + 3z

Combine like terms: -3z + 3z = 0
-6 + 1z + z2 = 0

Factor a trinomial.
(-3 + -1z)(2 + -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 '(2 + -1z)' equal to zero and attempt to solve:

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

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