6(3z-1)-5(z+9)=6(z+1)

Solution for 6(3z-1)-5(z+9)=6(z+1) equation:

Simplifying
6(3z + -1) + -5(z + 9) = 6(z + 1)

Reorder the terms:
6(-1 + 3z) + -5(z + 9) = 6(z + 1)
(-1 * 6 + 3z * 6) + -5(z + 9) = 6(z + 1)
(-6 + 18z) + -5(z + 9) = 6(z + 1)

Reorder the terms:
-6 + 18z + -5(9 + z) = 6(z + 1)
-6 + 18z + (9 * -5 + z * -5) = 6(z + 1)
-6 + 18z + (-45 + -5z) = 6(z + 1)

Reorder the terms:
-6 + -45 + 18z + -5z = 6(z + 1)

Combine like terms: -6 + -45 = -51
-51 + 18z + -5z = 6(z + 1)

Combine like terms: 18z + -5z = 13z
-51 + 13z = 6(z + 1)

Reorder the terms:
-51 + 13z = 6(1 + z)
-51 + 13z = (1 * 6 + z * 6)
-51 + 13z = (6 + 6z)

Solving
-51 + 13z = 6 + 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.
-51 + 13z + -6z = 6 + 6z + -6z

Combine like terms: 13z + -6z = 7z
-51 + 7z = 6 + 6z + -6z

Combine like terms: 6z + -6z = 0
-51 + 7z = 6 + 0
-51 + 7z = 6

Add '51' to each side of the equation.
-51 + 51 + 7z = 6 + 51

Combine like terms: -51 + 51 = 0
0 + 7z = 6 + 51
7z = 6 + 51

Combine like terms: 6 + 51 = 57
7z = 57

Divide each side by '7'.
z = 8.142857143

Simplifying
z = 8.142857143