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

Solution for 10(z+1)+2z=3(2z+1)+1 equation:

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

Reorder the terms:
10(1 + z) + 2z = 3(2z + 1) + 1
(1 * 10 + z * 10) + 2z = 3(2z + 1) + 1
(10 + 10z) + 2z = 3(2z + 1) + 1

Combine like terms: 10z + 2z = 12z
10 + 12z = 3(2z + 1) + 1

Reorder the terms:
10 + 12z = 3(1 + 2z) + 1
10 + 12z = (1 * 3 + 2z * 3) + 1
10 + 12z = (3 + 6z) + 1

Reorder the terms:
10 + 12z = 3 + 1 + 6z

Combine like terms: 3 + 1 = 4
10 + 12z = 4 + 6z

Solving
10 + 12z = 4 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
10 + 12z + -6z = 4 + 6z + -6z

Combine like terms: 12z + -6z = 6z
10 + 6z = 4 + 6z + -6z

Combine like terms: 6z + -6z = 0
10 + 6z = 4 + 0
10 + 6z = 4

Add '-10' to each side of the equation.
10 + -10 + 6z = 4 + -10

Combine like terms: 10 + -10 = 0
0 + 6z = 4 + -10
6z = 4 + -10

Combine like terms: 4 + -10 = -6
6z = -6

Divide each side by '6'.
z = -1

Simplifying
z = -1