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

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Solution for 9(z+1)-2(z-4)=2(z-4)+4(z-3) equation: 


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

Reorder the terms:
9(1 + z) + -2(z + -4) = 2(z + -4) + 4(z + -3)
(1 * 9 + z * 9) + -2(z + -4) = 2(z + -4) + 4(z + -3)
(9 + 9z) + -2(z + -4) = 2(z + -4) + 4(z + -3)

Reorder the terms:
9 + 9z + -2(-4 + z) = 2(z + -4) + 4(z + -3)
9 + 9z + (-4 * -2 + z * -2) = 2(z + -4) + 4(z + -3)
9 + 9z + (8 + -2z) = 2(z + -4) + 4(z + -3)

Reorder the terms:
9 + 8 + 9z + -2z = 2(z + -4) + 4(z + -3)

Combine like terms: 9 + 8 = 17
17 + 9z + -2z = 2(z + -4) + 4(z + -3)

Combine like terms: 9z + -2z = 7z
17 + 7z = 2(z + -4) + 4(z + -3)

Reorder the terms:
17 + 7z = 2(-4 + z) + 4(z + -3)
17 + 7z = (-4 * 2 + z * 2) + 4(z + -3)
17 + 7z = (-8 + 2z) + 4(z + -3)

Reorder the terms:
17 + 7z = -8 + 2z + 4(-3 + z)
17 + 7z = -8 + 2z + (-3 * 4 + z * 4)
17 + 7z = -8 + 2z + (-12 + 4z)

Reorder the terms:
17 + 7z = -8 + -12 + 2z + 4z

Combine like terms: -8 + -12 = -20
17 + 7z = -20 + 2z + 4z

Combine like terms: 2z + 4z = 6z
17 + 7z = -20 + 6z

Solving
17 + 7z = -20 + 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.
17 + 7z + -6z = -20 + 6z + -6z

Combine like terms: 7z + -6z = 1z
17 + 1z = -20 + 6z + -6z

Combine like terms: 6z + -6z = 0
17 + 1z = -20 + 0
17 + 1z = -20

Add '-17' to each side of the equation.
17 + -17 + 1z = -20 + -17

Combine like terms: 17 + -17 = 0
0 + 1z = -20 + -17
1z = -20 + -17

Combine like terms: -20 + -17 = -37
1z = -37

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

Simplifying
z = -37

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