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

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Solution for 10(z+1)-4(z-1)=2(z-1)+3(z-2) equation: 


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

Reorder the terms:
10(1 + z) + -4(z + -1) = 2(z + -1) + 3(z + -2)
(1 * 10 + z * 10) + -4(z + -1) = 2(z + -1) + 3(z + -2)
(10 + 10z) + -4(z + -1) = 2(z + -1) + 3(z + -2)

Reorder the terms:
10 + 10z + -4(-1 + z) = 2(z + -1) + 3(z + -2)
10 + 10z + (-1 * -4 + z * -4) = 2(z + -1) + 3(z + -2)
10 + 10z + (4 + -4z) = 2(z + -1) + 3(z + -2)

Reorder the terms:
10 + 4 + 10z + -4z = 2(z + -1) + 3(z + -2)

Combine like terms: 10 + 4 = 14
14 + 10z + -4z = 2(z + -1) + 3(z + -2)

Combine like terms: 10z + -4z = 6z
14 + 6z = 2(z + -1) + 3(z + -2)

Reorder the terms:
14 + 6z = 2(-1 + z) + 3(z + -2)
14 + 6z = (-1 * 2 + z * 2) + 3(z + -2)
14 + 6z = (-2 + 2z) + 3(z + -2)

Reorder the terms:
14 + 6z = -2 + 2z + 3(-2 + z)
14 + 6z = -2 + 2z + (-2 * 3 + z * 3)
14 + 6z = -2 + 2z + (-6 + 3z)

Reorder the terms:
14 + 6z = -2 + -6 + 2z + 3z

Combine like terms: -2 + -6 = -8
14 + 6z = -8 + 2z + 3z

Combine like terms: 2z + 3z = 5z
14 + 6z = -8 + 5z

Solving
14 + 6z = -8 + 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.
14 + 6z + -5z = -8 + 5z + -5z

Combine like terms: 6z + -5z = 1z
14 + 1z = -8 + 5z + -5z

Combine like terms: 5z + -5z = 0
14 + 1z = -8 + 0
14 + 1z = -8

Add '-14' to each side of the equation.
14 + -14 + 1z = -8 + -14

Combine like terms: 14 + -14 = 0
0 + 1z = -8 + -14
1z = -8 + -14

Combine like terms: -8 + -14 = -22
1z = -22

Divide each side by '1'.
z = -22

Simplifying
z = -22

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