7(z+1)-2(z-4)=2(z-1)+2(z-2)

Solution for 7(z+1)-2(z-4)=2(z-1)+2(z-2) equation:

Simplifying
7(z + 1) + -2(z + -4) = 2(z + -1) + 2(z + -2)

Reorder the terms:
7(1 + z) + -2(z + -4) = 2(z + -1) + 2(z + -2)
(1 * 7 + z * 7) + -2(z + -4) = 2(z + -1) + 2(z + -2)
(7 + 7z) + -2(z + -4) = 2(z + -1) + 2(z + -2)

Reorder the terms:
7 + 7z + -2(-4 + z) = 2(z + -1) + 2(z + -2)
7 + 7z + (-4 * -2 + z * -2) = 2(z + -1) + 2(z + -2)
7 + 7z + (8 + -2z) = 2(z + -1) + 2(z + -2)

Reorder the terms:
7 + 8 + 7z + -2z = 2(z + -1) + 2(z + -2)

Combine like terms: 7 + 8 = 15
15 + 7z + -2z = 2(z + -1) + 2(z + -2)

Combine like terms: 7z + -2z = 5z
15 + 5z = 2(z + -1) + 2(z + -2)

Reorder the terms:
15 + 5z = 2(-1 + z) + 2(z + -2)
15 + 5z = (-1 * 2 + z * 2) + 2(z + -2)
15 + 5z = (-2 + 2z) + 2(z + -2)

Reorder the terms:
15 + 5z = -2 + 2z + 2(-2 + z)
15 + 5z = -2 + 2z + (-2 * 2 + z * 2)
15 + 5z = -2 + 2z + (-4 + 2z)

Reorder the terms:
15 + 5z = -2 + -4 + 2z + 2z

Combine like terms: -2 + -4 = -6
15 + 5z = -6 + 2z + 2z

Combine like terms: 2z + 2z = 4z
15 + 5z = -6 + 4z

Solving
15 + 5z = -6 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
15 + 5z + -4z = -6 + 4z + -4z

Combine like terms: 5z + -4z = 1z
15 + 1z = -6 + 4z + -4z

Combine like terms: 4z + -4z = 0
15 + 1z = -6 + 0
15 + 1z = -6

Add '-15' to each side of the equation.
15 + -15 + 1z = -6 + -15

Combine like terms: 15 + -15 = 0
0 + 1z = -6 + -15
1z = -6 + -15

Combine like terms: -6 + -15 = -21
1z = -21

Divide each side by '1'.
z = -21

Simplifying
z = -21