8(z+1)-2(z-2)=2(z-3)+3(z-4)

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Solution for 8(z+1)-2(z-2)=2(z-3)+3(z-4) equation: 


Simplifying
8(z + 1) + -2(z + -2) = 2(z + -3) + 3(z + -4)

Reorder the terms:
8(1 + z) + -2(z + -2) = 2(z + -3) + 3(z + -4)
(1 * 8 + z * 8) + -2(z + -2) = 2(z + -3) + 3(z + -4)
(8 + 8z) + -2(z + -2) = 2(z + -3) + 3(z + -4)

Reorder the terms:
8 + 8z + -2(-2 + z) = 2(z + -3) + 3(z + -4)
8 + 8z + (-2 * -2 + z * -2) = 2(z + -3) + 3(z + -4)
8 + 8z + (4 + -2z) = 2(z + -3) + 3(z + -4)

Reorder the terms:
8 + 4 + 8z + -2z = 2(z + -3) + 3(z + -4)

Combine like terms: 8 + 4 = 12
12 + 8z + -2z = 2(z + -3) + 3(z + -4)

Combine like terms: 8z + -2z = 6z
12 + 6z = 2(z + -3) + 3(z + -4)

Reorder the terms:
12 + 6z = 2(-3 + z) + 3(z + -4)
12 + 6z = (-3 * 2 + z * 2) + 3(z + -4)
12 + 6z = (-6 + 2z) + 3(z + -4)

Reorder the terms:
12 + 6z = -6 + 2z + 3(-4 + z)
12 + 6z = -6 + 2z + (-4 * 3 + z * 3)
12 + 6z = -6 + 2z + (-12 + 3z)

Reorder the terms:
12 + 6z = -6 + -12 + 2z + 3z

Combine like terms: -6 + -12 = -18
12 + 6z = -18 + 2z + 3z

Combine like terms: 2z + 3z = 5z
12 + 6z = -18 + 5z

Solving
12 + 6z = -18 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
12 + 6z + -5z = -18 + 5z + -5z

Combine like terms: 6z + -5z = 1z
12 + 1z = -18 + 5z + -5z

Combine like terms: 5z + -5z = 0
12 + 1z = -18 + 0
12 + 1z = -18

Add '-12' to each side of the equation.
12 + -12 + 1z = -18 + -12

Combine like terms: 12 + -12 = 0
0 + 1z = -18 + -12
1z = -18 + -12

Combine like terms: -18 + -12 = -30
1z = -30

Divide each side by '1'.
z = -30

Simplifying
z = -30

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