7[9(8-a)-7]=9[7(9a-8)+6]-82

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Solution for 7[9(8-a)-7]=9[7(9a-8)+6]-82 equation: 


Simplifying
7[9(8 + -1a) + -7] = 9[7(9a + -8) + 6] + -82
7[(8 * 9 + -1a * 9) + -7] = 9[7(9a + -8) + 6] + -82
7[(72 + -9a) + -7] = 9[7(9a + -8) + 6] + -82

Reorder the terms:
7[72 + -7 + -9a] = 9[7(9a + -8) + 6] + -82

Combine like terms: 72 + -7 = 65
7[65 + -9a] = 9[7(9a + -8) + 6] + -82
[65 * 7 + -9a * 7] = 9[7(9a + -8) + 6] + -82
[455 + -63a] = 9[7(9a + -8) + 6] + -82

Reorder the terms:
455 + -63a = 9[7(-8 + 9a) + 6] + -82
455 + -63a = 9[(-8 * 7 + 9a * 7) + 6] + -82
455 + -63a = 9[(-56 + 63a) + 6] + -82

Reorder the terms:
455 + -63a = 9[-56 + 6 + 63a] + -82

Combine like terms: -56 + 6 = -50
455 + -63a = 9[-50 + 63a] + -82
455 + -63a = [-50 * 9 + 63a * 9] + -82
455 + -63a = [-450 + 567a] + -82

Reorder the terms:
455 + -63a = -450 + -82 + 567a

Combine like terms: -450 + -82 = -532
455 + -63a = -532 + 567a

Solving
455 + -63a = -532 + 567a

Solving for variable 'a'.

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

Add '-567a' to each side of the equation.
455 + -63a + -567a = -532 + 567a + -567a

Combine like terms: -63a + -567a = -630a
455 + -630a = -532 + 567a + -567a

Combine like terms: 567a + -567a = 0
455 + -630a = -532 + 0
455 + -630a = -532

Add '-455' to each side of the equation.
455 + -455 + -630a = -532 + -455

Combine like terms: 455 + -455 = 0
0 + -630a = -532 + -455
-630a = -532 + -455

Combine like terms: -532 + -455 = -987
-630a = -987

Divide each side by '-630'.
a = 1.566666667

Simplifying
a = 1.566666667

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