3z+2(6-z)=-(z-3)+1

Solution for 3z+2(6-z)=-(z-3)+1 equation:

Simplifying
3z + 2(6 + -1z) = -1(z + -3) + 1
3z + (6 * 2 + -1z * 2) = -1(z + -3) + 1
3z + (12 + -2z) = -1(z + -3) + 1

Reorder the terms:
12 + 3z + -2z = -1(z + -3) + 1

Combine like terms: 3z + -2z = 1z
12 + 1z = -1(z + -3) + 1

Reorder the terms:
12 + 1z = -1(-3 + z) + 1
12 + 1z = (-3 * -1 + z * -1) + 1
12 + 1z = (3 + -1z) + 1

Reorder the terms:
12 + 1z = 3 + 1 + -1z

Combine like terms: 3 + 1 = 4
12 + 1z = 4 + -1z

Solving
12 + 1z = 4 + -1z

Solving for variable 'z'.

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

Add 'z' to each side of the equation.
12 + 1z + z = 4 + -1z + z

Combine like terms: 1z + z = 2z
12 + 2z = 4 + -1z + z

Combine like terms: -1z + z = 0
12 + 2z = 4 + 0
12 + 2z = 4

Add '-12' to each side of the equation.
12 + -12 + 2z = 4 + -12

Combine like terms: 12 + -12 = 0
0 + 2z = 4 + -12
2z = 4 + -12

Combine like terms: 4 + -12 = -8
2z = -8

Divide each side by '2'.
z = -4

Simplifying
z = -4