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

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

Simplifying
9(z + 2) + -2(z + -3) = 3(z + -2) + 3(z + -3)
Reorder the terms:
9(2 + z) + -2(z + -3) = 3(z + -2) + 3(z + -3)
(2 * 9 + z * 9) + -2(z + -3) = 3(z + -2) + 3(z + -3)
(18 + 9z) + -2(z + -3) = 3(z + -2) + 3(z + -3)
Reorder the terms:
18 + 9z + -2(-3 + z) = 3(z + -2) + 3(z + -3)
18 + 9z + (-3 * -2 + z * -2) = 3(z + -2) + 3(z + -3)
18 + 9z + (6 + -2z) = 3(z + -2) + 3(z + -3)
Reorder the terms:
18 + 6 + 9z + -2z = 3(z + -2) + 3(z + -3)
Combine like terms: 18 + 6 = 24
24 + 9z + -2z = 3(z + -2) + 3(z + -3)
Combine like terms: 9z + -2z = 7z
24 + 7z = 3(z + -2) + 3(z + -3)
Reorder the terms:
24 + 7z = 3(-2 + z) + 3(z + -3)
24 + 7z = (-2 * 3 + z * 3) + 3(z + -3)
24 + 7z = (-6 + 3z) + 3(z + -3)
Reorder the terms:
24 + 7z = -6 + 3z + 3(-3 + z)
24 + 7z = -6 + 3z + (-3 * 3 + z * 3)
24 + 7z = -6 + 3z + (-9 + 3z)
Reorder the terms:
24 + 7z = -6 + -9 + 3z + 3z
Combine like terms: -6 + -9 = -15
24 + 7z = -15 + 3z + 3z
Combine like terms: 3z + 3z = 6z
24 + 7z = -15 + 6z
Solving
24 + 7z = -15 + 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 = -15 + 6z + -6z
Combine like terms: 7z + -6z = 1z
24 + 1z = -15 + 6z + -6z
Combine like terms: 6z + -6z = 0
24 + 1z = -15 + 0
24 + 1z = -15
Add '-24' to each side of the equation.
24 + -24 + 1z = -15 + -24
Combine like terms: 24 + -24 = 0
0 + 1z = -15 + -24
1z = -15 + -24
Combine like terms: -15 + -24 = -39
1z = -39
Divide each side by '1'.
z = -39
Simplifying
z = -39`