7(z+1)-2(z-3)=2(z-2)+2(z-2)

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Solution for 7(z+1)-2(z-3)=2(z-2)+2(z-2) equation: 


Simplifying
7(z + 1) + -2(z + -3) = 2(z + -2) + 2(z + -2)

Reorder the terms:
7(1 + z) + -2(z + -3) = 2(z + -2) + 2(z + -2)
(1 * 7 + z * 7) + -2(z + -3) = 2(z + -2) + 2(z + -2)
(7 + 7z) + -2(z + -3) = 2(z + -2) + 2(z + -2)

Reorder the terms:
7 + 7z + -2(-3 + z) = 2(z + -2) + 2(z + -2)
7 + 7z + (-3 * -2 + z * -2) = 2(z + -2) + 2(z + -2)
7 + 7z + (6 + -2z) = 2(z + -2) + 2(z + -2)

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

Combine like terms: 7 + 6 = 13
13 + 7z + -2z = 2(z + -2) + 2(z + -2)

Combine like terms: 7z + -2z = 5z
13 + 5z = 2(z + -2) + 2(z + -2)

Reorder the terms:
13 + 5z = 2(-2 + z) + 2(z + -2)
13 + 5z = (-2 * 2 + z * 2) + 2(z + -2)
13 + 5z = (-4 + 2z) + 2(z + -2)

Reorder the terms:
13 + 5z = -4 + 2z + 2(-2 + z)
13 + 5z = -4 + 2z + (-2 * 2 + z * 2)
13 + 5z = -4 + 2z + (-4 + 2z)

Reorder the terms:
13 + 5z = -4 + -4 + 2z + 2z

Combine like terms: -4 + -4 = -8
13 + 5z = -8 + 2z + 2z

Combine like terms: 2z + 2z = 4z
13 + 5z = -8 + 4z

Solving
13 + 5z = -8 + 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.
13 + 5z + -4z = -8 + 4z + -4z

Combine like terms: 5z + -4z = 1z
13 + 1z = -8 + 4z + -4z

Combine like terms: 4z + -4z = 0
13 + 1z = -8 + 0
13 + 1z = -8

Add '-13' to each side of the equation.
13 + -13 + 1z = -8 + -13

Combine like terms: 13 + -13 = 0
0 + 1z = -8 + -13
1z = -8 + -13

Combine like terms: -8 + -13 = -21
1z = -21

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

Simplifying
z = -21

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