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

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


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

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

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

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

Combine like terms: 10 + 4 = 14
14 + 10z + -2z = 4(z + -3) + 3(z + -4)

Combine like terms: 10z + -2z = 8z
14 + 8z = 4(z + -3) + 3(z + -4)

Reorder the terms:
14 + 8z = 4(-3 + z) + 3(z + -4)
14 + 8z = (-3 * 4 + z * 4) + 3(z + -4)
14 + 8z = (-12 + 4z) + 3(z + -4)

Reorder the terms:
14 + 8z = -12 + 4z + 3(-4 + z)
14 + 8z = -12 + 4z + (-4 * 3 + z * 3)
14 + 8z = -12 + 4z + (-12 + 3z)

Reorder the terms:
14 + 8z = -12 + -12 + 4z + 3z

Combine like terms: -12 + -12 = -24
14 + 8z = -24 + 4z + 3z

Combine like terms: 4z + 3z = 7z
14 + 8z = -24 + 7z

Solving
14 + 8z = -24 + 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.
14 + 8z + -7z = -24 + 7z + -7z

Combine like terms: 8z + -7z = 1z
14 + 1z = -24 + 7z + -7z

Combine like terms: 7z + -7z = 0
14 + 1z = -24 + 0
14 + 1z = -24

Add '-14' to each side of the equation.
14 + -14 + 1z = -24 + -14

Combine like terms: 14 + -14 = 0
0 + 1z = -24 + -14
1z = -24 + -14

Combine like terms: -24 + -14 = -38
1z = -38

Divide each side by '1'.
z = -38

Simplifying
z = -38

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