-(z+7)+(5z+1)=5(z+1)

Solution for -(z+7)+(5z+1)=5(z+1) equation:

Simplifying
-1(z + 7) + (5z + 1) = 5(z + 1)

Reorder the terms:
-1(7 + z) + (5z + 1) = 5(z + 1)
(7 * -1 + z * -1) + (5z + 1) = 5(z + 1)
(-7 + -1z) + (5z + 1) = 5(z + 1)

Reorder the terms:
-7 + -1z + (1 + 5z) = 5(z + 1)

Remove parenthesis around (1 + 5z)
-7 + -1z + 1 + 5z = 5(z + 1)

Reorder the terms:
-7 + 1 + -1z + 5z = 5(z + 1)

Combine like terms: -7 + 1 = -6
-6 + -1z + 5z = 5(z + 1)

Combine like terms: -1z + 5z = 4z
-6 + 4z = 5(z + 1)

Reorder the terms:
-6 + 4z = 5(1 + z)
-6 + 4z = (1 * 5 + z * 5)
-6 + 4z = (5 + 5z)

Solving
-6 + 4z = 5 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
-6 + 4z + -5z = 5 + 5z + -5z

Combine like terms: 4z + -5z = -1z
-6 + -1z = 5 + 5z + -5z

Combine like terms: 5z + -5z = 0
-6 + -1z = 5 + 0
-6 + -1z = 5

Add '6' to each side of the equation.
-6 + 6 + -1z = 5 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 5 + 6
-1z = 5 + 6

Combine like terms: 5 + 6 = 11
-1z = 11

Divide each side by '-1'.
z = -11

Simplifying
z = -11