(2z-3)(2+z)=z(2z-5)

Solution for (2z-3)(2+z)=z(2z-5) equation:

Simplifying
(2z + -3)(2 + z) = z(2z + -5)

Reorder the terms:
(-3 + 2z)(2 + z) = z(2z + -5)

Multiply (-3 + 2z) * (2 + z)
(-3(2 + z) + 2z * (2 + z)) = z(2z + -5)
((2 * -3 + z * -3) + 2z * (2 + z)) = z(2z + -5)
((-6 + -3z) + 2z * (2 + z)) = z(2z + -5)
(-6 + -3z + (2 * 2z + z * 2z)) = z(2z + -5)
(-6 + -3z + (4z + 2z2)) = z(2z + -5)

Combine like terms: -3z + 4z = 1z
(-6 + 1z + 2z2) = z(2z + -5)

Reorder the terms:
-6 + 1z + 2z2 = z(-5 + 2z)
-6 + 1z + 2z2 = (-5 * z + 2z * z)
-6 + 1z + 2z2 = (-5z + 2z2)

Add '-2z2' to each side of the equation.
-6 + 1z + 2z2 + -2z2 = -5z + 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-6 + 1z + 0 = -5z + 2z2 + -2z2
-6 + 1z = -5z + 2z2 + -2z2

Combine like terms: 2z2 + -2z2 = 0
-6 + 1z = -5z + 0
-6 + 1z = -5z

Solving
-6 + 1z = -5z

Solving for variable 'z'.

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

Add '5z' to each side of the equation.
-6 + 1z + 5z = -5z + 5z

Combine like terms: 1z + 5z = 6z
-6 + 6z = -5z + 5z

Combine like terms: -5z + 5z = 0
-6 + 6z = 0

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

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

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

Divide each side by '6'.
z = 1

Simplifying
z = 1