6(z+3)-5(3z+2)=2(z-9)

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Solution for 6(z+3)-5(3z+2)=2(z-9) equation:


Simplifying
6(z + 3) + -5(3z + 2) = 2(z + -9)

Reorder the terms:
6(3 + z) + -5(3z + 2) = 2(z + -9)
(3 * 6 + z * 6) + -5(3z + 2) = 2(z + -9)
(18 + 6z) + -5(3z + 2) = 2(z + -9)

Reorder the terms:
18 + 6z + -5(2 + 3z) = 2(z + -9)
18 + 6z + (2 * -5 + 3z * -5) = 2(z + -9)
18 + 6z + (-10 + -15z) = 2(z + -9)

Reorder the terms:
18 + -10 + 6z + -15z = 2(z + -9)

Combine like terms: 18 + -10 = 8
8 + 6z + -15z = 2(z + -9)

Combine like terms: 6z + -15z = -9z
8 + -9z = 2(z + -9)

Reorder the terms:
8 + -9z = 2(-9 + z)
8 + -9z = (-9 * 2 + z * 2)
8 + -9z = (-18 + 2z)

Solving
8 + -9z = -18 + 2z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-2z' to each side of the equation.
8 + -9z + -2z = -18 + 2z + -2z

Combine like terms: -9z + -2z = -11z
8 + -11z = -18 + 2z + -2z

Combine like terms: 2z + -2z = 0
8 + -11z = -18 + 0
8 + -11z = -18

Add '-8' to each side of the equation.
8 + -8 + -11z = -18 + -8

Combine like terms: 8 + -8 = 0
0 + -11z = -18 + -8
-11z = -18 + -8

Combine like terms: -18 + -8 = -26
-11z = -26

Divide each side by '-11'.
z = 2.363636364

Simplifying
z = 2.363636364

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