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

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


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

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

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

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

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

Combine like terms: 10z + -4z = 6z
32 + 6z = 3(z + -4) + 2(2 + -4)

Reorder the terms:
32 + 6z = 3(-4 + z) + 2(2 + -4)
32 + 6z = (-4 * 3 + z * 3) + 2(2 + -4)
32 + 6z = (-12 + 3z) + 2(2 + -4)

Combine like terms: 2 + -4 = -2
32 + 6z = -12 + 3z + 2(-2)

Multiply 2 * -2
32 + 6z = -12 + 3z + -4

Reorder the terms:
32 + 6z = -12 + -4 + 3z

Combine like terms: -12 + -4 = -16
32 + 6z = -16 + 3z

Solving
32 + 6z = -16 + 3z

Solving for variable 'z'.

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

Add '-3z' to each side of the equation.
32 + 6z + -3z = -16 + 3z + -3z

Combine like terms: 6z + -3z = 3z
32 + 3z = -16 + 3z + -3z

Combine like terms: 3z + -3z = 0
32 + 3z = -16 + 0
32 + 3z = -16

Add '-32' to each side of the equation.
32 + -32 + 3z = -16 + -32

Combine like terms: 32 + -32 = 0
0 + 3z = -16 + -32
3z = -16 + -32

Combine like terms: -16 + -32 = -48
3z = -48

Divide each side by '3'.
z = -16

Simplifying
z = -16

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