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

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


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

Reorder the terms:
10(2 + z) + -4(z + -1) = 3(x + -2) + 2(z + -1)
(2 * 10 + z * 10) + -4(z + -1) = 3(x + -2) + 2(z + -1)
(20 + 10z) + -4(z + -1) = 3(x + -2) + 2(z + -1)

Reorder the terms:
20 + 10z + -4(-1 + z) = 3(x + -2) + 2(z + -1)
20 + 10z + (-1 * -4 + z * -4) = 3(x + -2) + 2(z + -1)
20 + 10z + (4 + -4z) = 3(x + -2) + 2(z + -1)

Reorder the terms:
20 + 4 + 10z + -4z = 3(x + -2) + 2(z + -1)

Combine like terms: 20 + 4 = 24
24 + 10z + -4z = 3(x + -2) + 2(z + -1)

Combine like terms: 10z + -4z = 6z
24 + 6z = 3(x + -2) + 2(z + -1)

Reorder the terms:
24 + 6z = 3(-2 + x) + 2(z + -1)
24 + 6z = (-2 * 3 + x * 3) + 2(z + -1)
24 + 6z = (-6 + 3x) + 2(z + -1)

Reorder the terms:
24 + 6z = -6 + 3x + 2(-1 + z)
24 + 6z = -6 + 3x + (-1 * 2 + z * 2)
24 + 6z = -6 + 3x + (-2 + 2z)

Reorder the terms:
24 + 6z = -6 + -2 + 3x + 2z

Combine like terms: -6 + -2 = -8
24 + 6z = -8 + 3x + 2z

Solving
24 + 6z = -8 + 3x + 2z

Solving for variable 'z'.

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

Add '-2z' to each side of the equation.
24 + 6z + -2z = -8 + 3x + 2z + -2z

Combine like terms: 6z + -2z = 4z
24 + 4z = -8 + 3x + 2z + -2z

Combine like terms: 2z + -2z = 0
24 + 4z = -8 + 3x + 0
24 + 4z = -8 + 3x

Add '-24' to each side of the equation.
24 + -24 + 4z = -8 + -24 + 3x

Combine like terms: 24 + -24 = 0
0 + 4z = -8 + -24 + 3x
4z = -8 + -24 + 3x

Combine like terms: -8 + -24 = -32
4z = -32 + 3x

Divide each side by '4'.
z = -8 + 0.75x

Simplifying
z = -8 + 0.75x

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