(2z-1)(z-1)=z(z-5)

Solution for (2z-1)(z-1)=z(z-5) equation:

Simplifying
(2z + -1)(z + -1) = z(z + -5)

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

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

Multiply (-1 + 2z) * (-1 + z)
(-1(-1 + z) + 2z * (-1 + z)) = z(z + -5)
((-1 * -1 + z * -1) + 2z * (-1 + z)) = z(z + -5)
((1 + -1z) + 2z * (-1 + z)) = z(z + -5)
(1 + -1z + (-1 * 2z + z * 2z)) = z(z + -5)
(1 + -1z + (-2z + 2z2)) = z(z + -5)

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

Reorder the terms:
1 + -3z + 2z2 = z(-5 + z)
1 + -3z + 2z2 = (-5 * z + z * z)
1 + -3z + 2z2 = (-5z + z2)

Solving
1 + -3z + 2z2 = -5z + z2

Solving for variable 'z'.

Reorder the terms:
1 + -3z + 5z + 2z2 + -1z2 = -5z + z2 + 5z + -1z2

Combine like terms: -3z + 5z = 2z
1 + 2z + 2z2 + -1z2 = -5z + z2 + 5z + -1z2

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

Reorder the terms:
1 + 2z + 1z2 = -5z + 5z + z2 + -1z2

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

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

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

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

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

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

Simplifying
1 + z = 0

Solving
1 + z = 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 + z = 0 + -1

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

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

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