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

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


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

Reorder the terms:
9(2 + z) + -2(z + -3) = 3(z + -3) + 3(z + -4)
(2 * 9 + z * 9) + -2(z + -3) = 3(z + -3) + 3(z + -4)
(18 + 9z) + -2(z + -3) = 3(z + -3) + 3(z + -4)

Reorder the terms:
18 + 9z + -2(-3 + z) = 3(z + -3) + 3(z + -4)
18 + 9z + (-3 * -2 + z * -2) = 3(z + -3) + 3(z + -4)
18 + 9z + (6 + -2z) = 3(z + -3) + 3(z + -4)

Reorder the terms:
18 + 6 + 9z + -2z = 3(z + -3) + 3(z + -4)

Combine like terms: 18 + 6 = 24
24 + 9z + -2z = 3(z + -3) + 3(z + -4)

Combine like terms: 9z + -2z = 7z
24 + 7z = 3(z + -3) + 3(z + -4)

Reorder the terms:
24 + 7z = 3(-3 + z) + 3(z + -4)
24 + 7z = (-3 * 3 + z * 3) + 3(z + -4)
24 + 7z = (-9 + 3z) + 3(z + -4)

Reorder the terms:
24 + 7z = -9 + 3z + 3(-4 + z)
24 + 7z = -9 + 3z + (-4 * 3 + z * 3)
24 + 7z = -9 + 3z + (-12 + 3z)

Reorder the terms:
24 + 7z = -9 + -12 + 3z + 3z

Combine like terms: -9 + -12 = -21
24 + 7z = -21 + 3z + 3z

Combine like terms: 3z + 3z = 6z
24 + 7z = -21 + 6z

Solving
24 + 7z = -21 + 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.
24 + 7z + -6z = -21 + 6z + -6z

Combine like terms: 7z + -6z = 1z
24 + 1z = -21 + 6z + -6z

Combine like terms: 6z + -6z = 0
24 + 1z = -21 + 0
24 + 1z = -21

Add '-24' to each side of the equation.
24 + -24 + 1z = -21 + -24

Combine like terms: 24 + -24 = 0
0 + 1z = -21 + -24
1z = -21 + -24

Combine like terms: -21 + -24 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45

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