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

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


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

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

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

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

Combine like terms: 20 + 3 = 23
23 + 10z + -3z = 2(z + -1) + 4(z + -3)

Combine like terms: 10z + -3z = 7z
23 + 7z = 2(z + -1) + 4(z + -3)

Reorder the terms:
23 + 7z = 2(-1 + z) + 4(z + -3)
23 + 7z = (-1 * 2 + z * 2) + 4(z + -3)
23 + 7z = (-2 + 2z) + 4(z + -3)

Reorder the terms:
23 + 7z = -2 + 2z + 4(-3 + z)
23 + 7z = -2 + 2z + (-3 * 4 + z * 4)
23 + 7z = -2 + 2z + (-12 + 4z)

Reorder the terms:
23 + 7z = -2 + -12 + 2z + 4z

Combine like terms: -2 + -12 = -14
23 + 7z = -14 + 2z + 4z

Combine like terms: 2z + 4z = 6z
23 + 7z = -14 + 6z

Solving
23 + 7z = -14 + 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.
23 + 7z + -6z = -14 + 6z + -6z

Combine like terms: 7z + -6z = 1z
23 + 1z = -14 + 6z + -6z

Combine like terms: 6z + -6z = 0
23 + 1z = -14 + 0
23 + 1z = -14

Add '-23' to each side of the equation.
23 + -23 + 1z = -14 + -23

Combine like terms: 23 + -23 = 0
0 + 1z = -14 + -23
1z = -14 + -23

Combine like terms: -14 + -23 = -37
1z = -37

Divide each side by '1'.
z = -37

Simplifying
z = -37

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