2(4z-3)-3(5z+2)=4[10-(z+1)]

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Solution for 2(4z-3)-3(5z+2)=4[10-(z+1)] equation:


Simplifying
2(4z + -3) + -3(5z + 2) = 4[10 + -1(z + 1)]

Reorder the terms:
2(-3 + 4z) + -3(5z + 2) = 4[10 + -1(z + 1)]
(-3 * 2 + 4z * 2) + -3(5z + 2) = 4[10 + -1(z + 1)]
(-6 + 8z) + -3(5z + 2) = 4[10 + -1(z + 1)]

Reorder the terms:
-6 + 8z + -3(2 + 5z) = 4[10 + -1(z + 1)]
-6 + 8z + (2 * -3 + 5z * -3) = 4[10 + -1(z + 1)]
-6 + 8z + (-6 + -15z) = 4[10 + -1(z + 1)]

Reorder the terms:
-6 + -6 + 8z + -15z = 4[10 + -1(z + 1)]

Combine like terms: -6 + -6 = -12
-12 + 8z + -15z = 4[10 + -1(z + 1)]

Combine like terms: 8z + -15z = -7z
-12 + -7z = 4[10 + -1(z + 1)]

Reorder the terms:
-12 + -7z = 4[10 + -1(1 + z)]
-12 + -7z = 4[10 + (1 * -1 + z * -1)]
-12 + -7z = 4[10 + (-1 + -1z)]

Combine like terms: 10 + -1 = 9
-12 + -7z = 4[9 + -1z]
-12 + -7z = [9 * 4 + -1z * 4]
-12 + -7z = [36 + -4z]

Solving
-12 + -7z = 36 + -4z

Solving for variable 'z'.

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

Add '4z' to each side of the equation.
-12 + -7z + 4z = 36 + -4z + 4z

Combine like terms: -7z + 4z = -3z
-12 + -3z = 36 + -4z + 4z

Combine like terms: -4z + 4z = 0
-12 + -3z = 36 + 0
-12 + -3z = 36

Add '12' to each side of the equation.
-12 + 12 + -3z = 36 + 12

Combine like terms: -12 + 12 = 0
0 + -3z = 36 + 12
-3z = 36 + 12

Combine like terms: 36 + 12 = 48
-3z = 48

Divide each side by '-3'.
z = -16

Simplifying
z = -16

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