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

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


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

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

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

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

Combine like terms: 10 + 12 = 22
22 + 10z + -4z = 3(z + -4) + 2(2 + -4)

Combine like terms: 10z + -4z = 6z
22 + 6z = 3(z + -4) + 2(2 + -4)

Reorder the terms:
22 + 6z = 3(-4 + z) + 2(2 + -4)
22 + 6z = (-4 * 3 + z * 3) + 2(2 + -4)
22 + 6z = (-12 + 3z) + 2(2 + -4)

Combine like terms: 2 + -4 = -2
22 + 6z = -12 + 3z + 2(-2)

Multiply 2 * -2
22 + 6z = -12 + 3z + -4

Reorder the terms:
22 + 6z = -12 + -4 + 3z

Combine like terms: -12 + -4 = -16
22 + 6z = -16 + 3z

Solving
22 + 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.
22 + 6z + -3z = -16 + 3z + -3z

Combine like terms: 6z + -3z = 3z
22 + 3z = -16 + 3z + -3z

Combine like terms: 3z + -3z = 0
22 + 3z = -16 + 0
22 + 3z = -16

Add '-22' to each side of the equation.
22 + -22 + 3z = -16 + -22

Combine like terms: 22 + -22 = 0
0 + 3z = -16 + -22
3z = -16 + -22

Combine like terms: -16 + -22 = -38
3z = -38

Divide each side by '3'.
z = -12.66666667

Simplifying
z = -12.66666667

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