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

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


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

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

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

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

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

Combine like terms: 10z + -4z = 6z
14 + 6z = 2(z + -2) + (z + -3)

Reorder the terms:
14 + 6z = 2(-2 + z) + (z + -3)
14 + 6z = (-2 * 2 + z * 2) + (z + -3)
14 + 6z = (-4 + 2z) + (z + -3)

Reorder the terms:
14 + 6z = -4 + 2z + (-3 + z)

Remove parenthesis around (-3 + z)
14 + 6z = -4 + 2z + -3 + z

Reorder the terms:
14 + 6z = -4 + -3 + 2z + z

Combine like terms: -4 + -3 = -7
14 + 6z = -7 + 2z + z

Combine like terms: 2z + z = 3z
14 + 6z = -7 + 3z

Solving
14 + 6z = -7 + 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.
14 + 6z + -3z = -7 + 3z + -3z

Combine like terms: 6z + -3z = 3z
14 + 3z = -7 + 3z + -3z

Combine like terms: 3z + -3z = 0
14 + 3z = -7 + 0
14 + 3z = -7

Add '-14' to each side of the equation.
14 + -14 + 3z = -7 + -14

Combine like terms: 14 + -14 = 0
0 + 3z = -7 + -14
3z = -7 + -14

Combine like terms: -7 + -14 = -21
3z = -21

Divide each side by '3'.
z = -7

Simplifying
z = -7

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