(z-1)(z-1)+5(z-1)-50=0

Solution for (z-1)(z-1)+5(z-1)-50=0 equation:

Simplifying
(z + -1)(z + -1) + 5(z + -1) + -50 = 0

Reorder the terms:
(-1 + z)(z + -1) + 5(z + -1) + -50 = 0

Reorder the terms:
(-1 + z)(-1 + z) + 5(z + -1) + -50 = 0

Multiply (-1 + z) * (-1 + z)
(-1(-1 + z) + z(-1 + z)) + 5(z + -1) + -50 = 0
((-1 * -1 + z * -1) + z(-1 + z)) + 5(z + -1) + -50 = 0
((1 + -1z) + z(-1 + z)) + 5(z + -1) + -50 = 0
(1 + -1z + (-1 * z + z * z)) + 5(z + -1) + -50 = 0
(1 + -1z + (-1z + z2)) + 5(z + -1) + -50 = 0

Combine like terms: -1z + -1z = -2z
(1 + -2z + z2) + 5(z + -1) + -50 = 0

Reorder the terms:
1 + -2z + z2 + 5(-1 + z) + -50 = 0
1 + -2z + z2 + (-1 * 5 + z * 5) + -50 = 0
1 + -2z + z2 + (-5 + 5z) + -50 = 0

Reorder the terms:
1 + -5 + -50 + -2z + 5z + z2 = 0

Combine like terms: 1 + -5 = -4
-4 + -50 + -2z + 5z + z2 = 0

Combine like terms: -4 + -50 = -54
-54 + -2z + 5z + z2 = 0

Combine like terms: -2z + 5z = 3z
-54 + 3z + z2 = 0

Solving
-54 + 3z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-9 + -1z)(6 + -1z) = 0

Subproblem 1
Set the factor '(-9 + -1z)' equal to zero and attempt to solve:

Simplifying
-9 + -1z = 0

Solving
-9 + -1z = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1z = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1z = 0 + 9
-1z = 0 + 9

Combine like terms: 0 + 9 = 9
-1z = 9

Divide each side by '-1'.
z = -9

Simplifying
z = -9
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 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 + -1z = 0 + -6

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

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

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-9, 6}