(6+-1(5+-1z)+-1z)+3(5+-1z)+1z=10

Solution for (6+-1(5+-1z)+-1z)+3(5+-1z)+1z=10 equation:

Simplifying
(6 + -1(5 + -1z) + -1z) + 3(5 + -1z) + 1z = 10
(6 + (5 * -1 + -1z * -1) + -1z) + 3(5 + -1z) + 1z = 10
(6 + (-5 + 1z) + -1z) + 3(5 + -1z) + 1z = 10

Combine like terms: 6 + -5 = 1
(1 + 1z + -1z) + 3(5 + -1z) + 1z = 10

Combine like terms: 1z + -1z = 0
(1 + 0) + 3(5 + -1z) + 1z = 10
(1) + 3(5 + -1z) + 1z = 10
1 + 3(5 + -1z) + 1z = 10
1 + (5 * 3 + -1z * 3) + 1z = 10
1 + (15 + -3z) + 1z = 10

Combine like terms: 1 + 15 = 16
16 + -3z + 1z = 10

Combine like terms: -3z + 1z = -2z
16 + -2z = 10

Solving
16 + -2z = 10

Solving for variable 'z'.

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

Add '-16' to each side of the equation.
16 + -16 + -2z = 10 + -16

Combine like terms: 16 + -16 = 0
0 + -2z = 10 + -16
-2z = 10 + -16

Combine like terms: 10 + -16 = -6
-2z = -6

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

Simplifying
z = 3