z^2=(2z-3)(z-2)

Solution for z^2=(2z-3)(z-2) equation:

Simplifying
z2 = (2z + -3)(z + -2)

Reorder the terms:
z2 = (-3 + 2z)(z + -2)

Reorder the terms:
z2 = (-3 + 2z)(-2 + z)

Multiply (-3 + 2z) * (-2 + z)
z2 = (-3(-2 + z) + 2z * (-2 + z))
z2 = ((-2 * -3 + z * -3) + 2z * (-2 + z))
z2 = ((6 + -3z) + 2z * (-2 + z))
z2 = (6 + -3z + (-2 * 2z + z * 2z))
z2 = (6 + -3z + (-4z + 2z2))

Combine like terms: -3z + -4z = -7z
z2 = (6 + -7z + 2z2)

Solving
z2 = 6 + -7z + 2z2

Solving for variable 'z'.

Reorder the terms:
-6 + 7z + z2 + -2z2 = 6 + -7z + 2z2 + -6 + 7z + -2z2

Combine like terms: z2 + -2z2 = -1z2
-6 + 7z + -1z2 = 6 + -7z + 2z2 + -6 + 7z + -2z2

Reorder the terms:
-6 + 7z + -1z2 = 6 + -6 + -7z + 7z + 2z2 + -2z2

Combine like terms: 6 + -6 = 0
-6 + 7z + -1z2 = 0 + -7z + 7z + 2z2 + -2z2
-6 + 7z + -1z2 = -7z + 7z + 2z2 + -2z2

Combine like terms: -7z + 7z = 0
-6 + 7z + -1z2 = 0 + 2z2 + -2z2
-6 + 7z + -1z2 = 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-6 + 7z + -1z2 = 0

Factor a trinomial.
(-6 + z)(1 + -1z) = 0

Subproblem 1
Set the factor '(-6 + z)' equal to zero and attempt to solve:

Simplifying
-6 + z = 0

Solving
-6 + z = 0

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

Add '6' to each side of the equation.
-6 + 6 + z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + z = 0 + 6
z = 0 + 6

Combine like terms: 0 + 6 = 6
z = 6

Simplifying
z = 6
Subproblem 2
Set the factor '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Solution
z = {6, 1}