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

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

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

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

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

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

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

Reorder the terms:
-6 + -1z + z2 = -3 + 2z

Solving
-6 + -1z + z2 = -3 + 2z

Solving for variable 'z'.

Reorder the terms:
-6 + 3 + -1z + -2z + z2 = -3 + 2z + 3 + -2z

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

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

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

Combine like terms: -3 + 3 = 0
-3 + -3z + z2 = 0 + 2z + -2z
-3 + -3z + z2 = 2z + -2z

Combine like terms: 2z + -2z = 0
-3 + -3z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -3z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + -3z + z2 = 0 + 3

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

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

The z term is -3z.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3z + 2.25 + z2 = 3 + 2.25

Reorder the terms:
2.25 + -3z + z2 = 3 + 2.25

Combine like terms: 3 + 2.25 = 5.25
2.25 + -3z + z2 = 5.25

Factor a perfect square on the left side:
(z + -1.5)(z + -1.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(z + -1.5) equal to 2.291287847 and -2.291287847.

Subproblem 1
z + -1.5 = 2.291287847

Simplifying
z + -1.5 = 2.291287847

Reorder the terms:
-1.5 + z = 2.291287847

Solving
-1.5 + z = 2.291287847

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z = 2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = 2.291287847 + 1.5
z = 2.291287847 + 1.5

Combine like terms: 2.291287847 + 1.5 = 3.791287847
z = 3.791287847

Simplifying
z = 3.791287847

Subproblem 2
z + -1.5 = -2.291287847

Simplifying
z + -1.5 = -2.291287847

Reorder the terms:
-1.5 + z = -2.291287847

Solving
-1.5 + z = -2.291287847

Solving for variable 'z'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + z = -2.291287847 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + z = -2.291287847 + 1.5
z = -2.291287847 + 1.5

Combine like terms: -2.291287847 + 1.5 = -0.791287847
z = -0.791287847

Simplifying
z = -0.791287847

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {3.791287847, -0.791287847}