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

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


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

Reorder the terms:
10(2 + z) + -2(z + -4) = 4(z + -2) + 3(z + -2)
(2 * 10 + z * 10) + -2(z + -4) = 4(z + -2) + 3(z + -2)
(20 + 10z) + -2(z + -4) = 4(z + -2) + 3(z + -2)

Reorder the terms:
20 + 10z + -2(-4 + z) = 4(z + -2) + 3(z + -2)
20 + 10z + (-4 * -2 + z * -2) = 4(z + -2) + 3(z + -2)
20 + 10z + (8 + -2z) = 4(z + -2) + 3(z + -2)

Reorder the terms:
20 + 8 + 10z + -2z = 4(z + -2) + 3(z + -2)

Combine like terms: 20 + 8 = 28
28 + 10z + -2z = 4(z + -2) + 3(z + -2)

Combine like terms: 10z + -2z = 8z
28 + 8z = 4(z + -2) + 3(z + -2)

Reorder the terms:
28 + 8z = 4(-2 + z) + 3(z + -2)
28 + 8z = (-2 * 4 + z * 4) + 3(z + -2)
28 + 8z = (-8 + 4z) + 3(z + -2)

Reorder the terms:
28 + 8z = -8 + 4z + 3(-2 + z)
28 + 8z = -8 + 4z + (-2 * 3 + z * 3)
28 + 8z = -8 + 4z + (-6 + 3z)

Reorder the terms:
28 + 8z = -8 + -6 + 4z + 3z

Combine like terms: -8 + -6 = -14
28 + 8z = -14 + 4z + 3z

Combine like terms: 4z + 3z = 7z
28 + 8z = -14 + 7z

Solving
28 + 8z = -14 + 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.
28 + 8z + -7z = -14 + 7z + -7z

Combine like terms: 8z + -7z = 1z
28 + 1z = -14 + 7z + -7z

Combine like terms: 7z + -7z = 0
28 + 1z = -14 + 0
28 + 1z = -14

Add '-28' to each side of the equation.
28 + -28 + 1z = -14 + -28

Combine like terms: 28 + -28 = 0
0 + 1z = -14 + -28
1z = -14 + -28

Combine like terms: -14 + -28 = -42
1z = -42

Divide each side by '1'.
z = -42

Simplifying
z = -42

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