-(z+8)+(5z+1)=3(z+1)

Solution for -(z+8)+(5z+1)=3(z+1) equation:

Simplifying
-1(z + 8) + (5z + 1) = 3(z + 1)

Reorder the terms:
-1(8 + z) + (5z + 1) = 3(z + 1)
(8 * -1 + z * -1) + (5z + 1) = 3(z + 1)
(-8 + -1z) + (5z + 1) = 3(z + 1)

Reorder the terms:
-8 + -1z + (1 + 5z) = 3(z + 1)

Remove parenthesis around (1 + 5z)
-8 + -1z + 1 + 5z = 3(z + 1)

Reorder the terms:
-8 + 1 + -1z + 5z = 3(z + 1)

Combine like terms: -8 + 1 = -7
-7 + -1z + 5z = 3(z + 1)

Combine like terms: -1z + 5z = 4z
-7 + 4z = 3(z + 1)

Reorder the terms:
-7 + 4z = 3(1 + z)
-7 + 4z = (1 * 3 + z * 3)
-7 + 4z = (3 + 3z)

Solving
-7 + 4z = 3 + 3z

Solving for variable 'z'.

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

Add '-3z' to each side of the equation.
-7 + 4z + -3z = 3 + 3z + -3z

Combine like terms: 4z + -3z = 1z
-7 + 1z = 3 + 3z + -3z

Combine like terms: 3z + -3z = 0
-7 + 1z = 3 + 0
-7 + 1z = 3

Add '7' to each side of the equation.
-7 + 7 + 1z = 3 + 7

Combine like terms: -7 + 7 = 0
0 + 1z = 3 + 7
1z = 3 + 7

Combine like terms: 3 + 7 = 10
1z = 10

Divide each side by '1'.
z = 10

Simplifying
z = 10