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

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


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

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

Reorder the terms:
20 + 10z + -3(-4 + z) = 4(z + -2) + 2(z + -2)
20 + 10z + (-4 * -3 + z * -3) = 4(z + -2) + 2(z + -2)
20 + 10z + (12 + -3z) = 4(z + -2) + 2(z + -2)

Reorder the terms:
20 + 12 + 10z + -3z = 4(z + -2) + 2(z + -2)

Combine like terms: 20 + 12 = 32
32 + 10z + -3z = 4(z + -2) + 2(z + -2)

Combine like terms: 10z + -3z = 7z
32 + 7z = 4(z + -2) + 2(z + -2)

Reorder the terms:
32 + 7z = 4(-2 + z) + 2(z + -2)
32 + 7z = (-2 * 4 + z * 4) + 2(z + -2)
32 + 7z = (-8 + 4z) + 2(z + -2)

Reorder the terms:
32 + 7z = -8 + 4z + 2(-2 + z)
32 + 7z = -8 + 4z + (-2 * 2 + z * 2)
32 + 7z = -8 + 4z + (-4 + 2z)

Reorder the terms:
32 + 7z = -8 + -4 + 4z + 2z

Combine like terms: -8 + -4 = -12
32 + 7z = -12 + 4z + 2z

Combine like terms: 4z + 2z = 6z
32 + 7z = -12 + 6z

Solving
32 + 7z = -12 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
32 + 7z + -6z = -12 + 6z + -6z

Combine like terms: 7z + -6z = 1z
32 + 1z = -12 + 6z + -6z

Combine like terms: 6z + -6z = 0
32 + 1z = -12 + 0
32 + 1z = -12

Add '-32' to each side of the equation.
32 + -32 + 1z = -12 + -32

Combine like terms: 32 + -32 = 0
0 + 1z = -12 + -32
1z = -12 + -32

Combine like terms: -12 + -32 = -44
1z = -44

Divide each side by '1'.
z = -44

Simplifying
z = -44

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