z(z-1)=(z+3)(z-2)

Solution for z(z-1)=(z+3)(z-2) equation:

Simplifying
z(z + -1) = (z + 3)(z + -2)

Reorder the terms:
z(-1 + z) = (z + 3)(z + -2)
(-1 * z + z * z) = (z + 3)(z + -2)
(-1z + z2) = (z + 3)(z + -2)

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

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

Multiply (3 + z) * (-2 + z)
-1z + z2 = (3(-2 + z) + z(-2 + z))
-1z + z2 = ((-2 * 3 + z * 3) + z(-2 + z))
-1z + z2 = ((-6 + 3z) + z(-2 + z))
-1z + z2 = (-6 + 3z + (-2 * z + z * z))
-1z + z2 = (-6 + 3z + (-2z + z2))

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

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

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

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

Solving
-1z = -6 + 1z

Solving for variable 'z'.

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

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

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

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

Divide each side by '-2'.
z = 3

Simplifying
z = 3