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

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

Simplifying
-1(z + 6) + (3z + 1) = -3(z + 1)

Reorder the terms:
-1(6 + z) + (3z + 1) = -3(z + 1)
(6 * -1 + z * -1) + (3z + 1) = -3(z + 1)
(-6 + -1z) + (3z + 1) = -3(z + 1)

Reorder the terms:
-6 + -1z + (1 + 3z) = -3(z + 1)

Remove parenthesis around (1 + 3z)
-6 + -1z + 1 + 3z = -3(z + 1)

Reorder the terms:
-6 + 1 + -1z + 3z = -3(z + 1)

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

Combine like terms: -1z + 3z = 2z
-5 + 2z = -3(z + 1)

Reorder the terms:
-5 + 2z = -3(1 + z)
-5 + 2z = (1 * -3 + z * -3)
-5 + 2z = (-3 + -3z)

Solving
-5 + 2z = -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.
-5 + 2z + 3z = -3 + -3z + 3z

Combine like terms: 2z + 3z = 5z
-5 + 5z = -3 + -3z + 3z

Combine like terms: -3z + 3z = 0
-5 + 5z = -3 + 0
-5 + 5z = -3

Add '5' to each side of the equation.
-5 + 5 + 5z = -3 + 5

Combine like terms: -5 + 5 = 0
0 + 5z = -3 + 5
5z = -3 + 5

Combine like terms: -3 + 5 = 2
5z = 2

Divide each side by '5'.
z = 0.4

Simplifying
z = 0.4