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

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


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

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

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

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

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

Combine like terms: 10z + -4z = 6z
28 + 6z = 2(z + -4) + 3(z + -3)

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

Reorder the terms:
28 + 6z = -8 + 2z + 3(-3 + z)
28 + 6z = -8 + 2z + (-3 * 3 + z * 3)
28 + 6z = -8 + 2z + (-9 + 3z)

Reorder the terms:
28 + 6z = -8 + -9 + 2z + 3z

Combine like terms: -8 + -9 = -17
28 + 6z = -17 + 2z + 3z

Combine like terms: 2z + 3z = 5z
28 + 6z = -17 + 5z

Solving
28 + 6z = -17 + 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.
28 + 6z + -5z = -17 + 5z + -5z

Combine like terms: 6z + -5z = 1z
28 + 1z = -17 + 5z + -5z

Combine like terms: 5z + -5z = 0
28 + 1z = -17 + 0
28 + 1z = -17

Add '-28' to each side of the equation.
28 + -28 + 1z = -17 + -28

Combine like terms: 28 + -28 = 0
0 + 1z = -17 + -28
1z = -17 + -28

Combine like terms: -17 + -28 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45

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