6(2z+1)-2(z+5)=7(z+1)

Solution for 6(2z+1)-2(z+5)=7(z+1) equation:

Simplifying
6(2z + 1) + -2(z + 5) = 7(z + 1)

Reorder the terms:
6(1 + 2z) + -2(z + 5) = 7(z + 1)
(1 * 6 + 2z * 6) + -2(z + 5) = 7(z + 1)
(6 + 12z) + -2(z + 5) = 7(z + 1)

Reorder the terms:
6 + 12z + -2(5 + z) = 7(z + 1)
6 + 12z + (5 * -2 + z * -2) = 7(z + 1)
6 + 12z + (-10 + -2z) = 7(z + 1)

Reorder the terms:
6 + -10 + 12z + -2z = 7(z + 1)

Combine like terms: 6 + -10 = -4
-4 + 12z + -2z = 7(z + 1)

Combine like terms: 12z + -2z = 10z
-4 + 10z = 7(z + 1)

Reorder the terms:
-4 + 10z = 7(1 + z)
-4 + 10z = (1 * 7 + z * 7)
-4 + 10z = (7 + 7z)

Solving
-4 + 10z = 7 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
-4 + 10z + -7z = 7 + 7z + -7z

Combine like terms: 10z + -7z = 3z
-4 + 3z = 7 + 7z + -7z

Combine like terms: 7z + -7z = 0
-4 + 3z = 7 + 0
-4 + 3z = 7

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

Combine like terms: -4 + 4 = 0
0 + 3z = 7 + 4
3z = 7 + 4

Combine like terms: 7 + 4 = 11
3z = 11

Divide each side by '3'.
z = 3.666666667

Simplifying
z = 3.666666667