6(4z-1)-4(z+9)=7(z+1)

Solution for 6(4z-1)-4(z+9)=7(z+1) equation:

Simplifying
6(4z + -1) + -4(z + 9) = 7(z + 1)

Reorder the terms:
6(-1 + 4z) + -4(z + 9) = 7(z + 1)
(-1 * 6 + 4z * 6) + -4(z + 9) = 7(z + 1)
(-6 + 24z) + -4(z + 9) = 7(z + 1)

Reorder the terms:
-6 + 24z + -4(9 + z) = 7(z + 1)
-6 + 24z + (9 * -4 + z * -4) = 7(z + 1)
-6 + 24z + (-36 + -4z) = 7(z + 1)

Reorder the terms:
-6 + -36 + 24z + -4z = 7(z + 1)

Combine like terms: -6 + -36 = -42
-42 + 24z + -4z = 7(z + 1)

Combine like terms: 24z + -4z = 20z
-42 + 20z = 7(z + 1)

Reorder the terms:
-42 + 20z = 7(1 + z)
-42 + 20z = (1 * 7 + z * 7)
-42 + 20z = (7 + 7z)

Solving
-42 + 20z = 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.
-42 + 20z + -7z = 7 + 7z + -7z

Combine like terms: 20z + -7z = 13z
-42 + 13z = 7 + 7z + -7z

Combine like terms: 7z + -7z = 0
-42 + 13z = 7 + 0
-42 + 13z = 7

Add '42' to each side of the equation.
-42 + 42 + 13z = 7 + 42

Combine like terms: -42 + 42 = 0
0 + 13z = 7 + 42
13z = 7 + 42

Combine like terms: 7 + 42 = 49
13z = 49

Divide each side by '13'.
z = 3.769230769

Simplifying
z = 3.769230769