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

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


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

Reorder the terms:
10(4 + z) + -2(z + -3) = 3(z + -1) + 4(z + -2)
(4 * 10 + z * 10) + -2(z + -3) = 3(z + -1) + 4(z + -2)
(40 + 10z) + -2(z + -3) = 3(z + -1) + 4(z + -2)

Reorder the terms:
40 + 10z + -2(-3 + z) = 3(z + -1) + 4(z + -2)
40 + 10z + (-3 * -2 + z * -2) = 3(z + -1) + 4(z + -2)
40 + 10z + (6 + -2z) = 3(z + -1) + 4(z + -2)

Reorder the terms:
40 + 6 + 10z + -2z = 3(z + -1) + 4(z + -2)

Combine like terms: 40 + 6 = 46
46 + 10z + -2z = 3(z + -1) + 4(z + -2)

Combine like terms: 10z + -2z = 8z
46 + 8z = 3(z + -1) + 4(z + -2)

Reorder the terms:
46 + 8z = 3(-1 + z) + 4(z + -2)
46 + 8z = (-1 * 3 + z * 3) + 4(z + -2)
46 + 8z = (-3 + 3z) + 4(z + -2)

Reorder the terms:
46 + 8z = -3 + 3z + 4(-2 + z)
46 + 8z = -3 + 3z + (-2 * 4 + z * 4)
46 + 8z = -3 + 3z + (-8 + 4z)

Reorder the terms:
46 + 8z = -3 + -8 + 3z + 4z

Combine like terms: -3 + -8 = -11
46 + 8z = -11 + 3z + 4z

Combine like terms: 3z + 4z = 7z
46 + 8z = -11 + 7z

Solving
46 + 8z = -11 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
46 + 8z + -7z = -11 + 7z + -7z

Combine like terms: 8z + -7z = 1z
46 + 1z = -11 + 7z + -7z

Combine like terms: 7z + -7z = 0
46 + 1z = -11 + 0
46 + 1z = -11

Add '-46' to each side of the equation.
46 + -46 + 1z = -11 + -46

Combine like terms: 46 + -46 = 0
0 + 1z = -11 + -46
1z = -11 + -46

Combine like terms: -11 + -46 = -57
1z = -57

Divide each side by '1'.
z = -57

Simplifying
z = -57

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