3[5-3(4-z)]-5=5[3(5z-4)+2]-27

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Solution for 3[5-3(4-z)]-5=5[3(5z-4)+2]-27 equation: 


Simplifying
3[5 + -3(4 + -1z)] + -5 = 5[3(5z + -4) + 2] + -27
3[5 + (4 * -3 + -1z * -3)] + -5 = 5[3(5z + -4) + 2] + -27
3[5 + (-12 + 3z)] + -5 = 5[3(5z + -4) + 2] + -27

Combine like terms: 5 + -12 = -7
3[-7 + 3z] + -5 = 5[3(5z + -4) + 2] + -27
[-7 * 3 + 3z * 3] + -5 = 5[3(5z + -4) + 2] + -27
[-21 + 9z] + -5 = 5[3(5z + -4) + 2] + -27

Reorder the terms:
-21 + -5 + 9z = 5[3(5z + -4) + 2] + -27

Combine like terms: -21 + -5 = -26
-26 + 9z = 5[3(5z + -4) + 2] + -27

Reorder the terms:
-26 + 9z = 5[3(-4 + 5z) + 2] + -27
-26 + 9z = 5[(-4 * 3 + 5z * 3) + 2] + -27
-26 + 9z = 5[(-12 + 15z) + 2] + -27

Reorder the terms:
-26 + 9z = 5[-12 + 2 + 15z] + -27

Combine like terms: -12 + 2 = -10
-26 + 9z = 5[-10 + 15z] + -27
-26 + 9z = [-10 * 5 + 15z * 5] + -27
-26 + 9z = [-50 + 75z] + -27

Reorder the terms:
-26 + 9z = -50 + -27 + 75z

Combine like terms: -50 + -27 = -77
-26 + 9z = -77 + 75z

Solving
-26 + 9z = -77 + 75z

Solving for variable 'z'.

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

Add '-75z' to each side of the equation.
-26 + 9z + -75z = -77 + 75z + -75z

Combine like terms: 9z + -75z = -66z
-26 + -66z = -77 + 75z + -75z

Combine like terms: 75z + -75z = 0
-26 + -66z = -77 + 0
-26 + -66z = -77

Add '26' to each side of the equation.
-26 + 26 + -66z = -77 + 26

Combine like terms: -26 + 26 = 0
0 + -66z = -77 + 26
-66z = -77 + 26

Combine like terms: -77 + 26 = -51
-66z = -51

Divide each side by '-66'.
z = 0.7727272727

Simplifying
z = 0.7727272727

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