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

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

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

Reorder the terms:
2(-3 + z) + 1 = z + -2(z + 1)
(-3 * 2 + z * 2) + 1 = z + -2(z + 1)
(-6 + 2z) + 1 = z + -2(z + 1)

Reorder the terms:
-6 + 1 + 2z = z + -2(z + 1)

Combine like terms: -6 + 1 = -5
-5 + 2z = z + -2(z + 1)

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

Reorder the terms:
-5 + 2z = -2 + z + -2z

Combine like terms: z + -2z = -1z
-5 + 2z = -2 + -1z

Solving
-5 + 2z = -2 + -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.
-5 + 2z + z = -2 + -1z + z

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

Combine like terms: -1z + z = 0
-5 + 3z = -2 + 0
-5 + 3z = -2

Add '5' to each side of the equation.
-5 + 5 + 3z = -2 + 5

Combine like terms: -5 + 5 = 0
0 + 3z = -2 + 5
3z = -2 + 5

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

Divide each side by '3'.
z = 1

Simplifying
z = 1