(z-1)+(z+1)2-52=0

Solution for (z-1)+(z+1)2-52=0 equation:

Simplifying
(z + -1) + (z + 1) * 2 + -52 = 0

Reorder the terms:
(-1 + z) + (z + 1) * 2 + -52 = 0

Remove parenthesis around (-1 + z)
-1 + z + (z + 1) * 2 + -52 = 0

Reorder the terms:
-1 + z + (1 + z) * 2 + -52 = 0

Reorder the terms for easier multiplication:
-1 + z + 2(1 + z) + -52 = 0
-1 + z + (1 * 2 + z * 2) + -52 = 0
-1 + z + (2 + 2z) + -52 = 0

Reorder the terms:
-1 + 2 + -52 + z + 2z = 0

Combine like terms: -1 + 2 = 1
1 + -52 + z + 2z = 0

Combine like terms: 1 + -52 = -51
-51 + z + 2z = 0

Combine like terms: z + 2z = 3z
-51 + 3z = 0

Solving
-51 + 3z = 0

Solving for variable 'z'.

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

Add '51' to each side of the equation.
-51 + 51 + 3z = 0 + 51

Combine like terms: -51 + 51 = 0
0 + 3z = 0 + 51
3z = 0 + 51

Combine like terms: 0 + 51 = 51
3z = 51

Divide each side by '3'.
z = 17

Simplifying
z = 17