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

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


Simplifying
7[9 + -7(8 + -1b)] + -9 = 9[(9b + -8) + 6] + -82
7[9 + (8 * -7 + -1b * -7)] + -9 = 9[(9b + -8) + 6] + -82
7[9 + (-56 + 7b)] + -9 = 9[(9b + -8) + 6] + -82

Combine like terms: 9 + -56 = -47
7[-47 + 7b] + -9 = 9[(9b + -8) + 6] + -82
[-47 * 7 + 7b * 7] + -9 = 9[(9b + -8) + 6] + -82
[-329 + 49b] + -9 = 9[(9b + -8) + 6] + -82

Reorder the terms:
-329 + -9 + 49b = 9[(9b + -8) + 6] + -82

Combine like terms: -329 + -9 = -338
-338 + 49b = 9[(9b + -8) + 6] + -82

Reorder the terms:
-338 + 49b = 9[(-8 + 9b) + 6] + -82

Remove parenthesis around (-8 + 9b)
-338 + 49b = 9[-8 + 9b + 6] + -82

Reorder the terms:
-338 + 49b = 9[-8 + 6 + 9b] + -82

Combine like terms: -8 + 6 = -2
-338 + 49b = 9[-2 + 9b] + -82
-338 + 49b = [-2 * 9 + 9b * 9] + -82
-338 + 49b = [-18 + 81b] + -82

Reorder the terms:
-338 + 49b = -18 + -82 + 81b

Combine like terms: -18 + -82 = -100
-338 + 49b = -100 + 81b

Solving
-338 + 49b = -100 + 81b

Solving for variable 'b'.

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

Add '-81b' to each side of the equation.
-338 + 49b + -81b = -100 + 81b + -81b

Combine like terms: 49b + -81b = -32b
-338 + -32b = -100 + 81b + -81b

Combine like terms: 81b + -81b = 0
-338 + -32b = -100 + 0
-338 + -32b = -100

Add '338' to each side of the equation.
-338 + 338 + -32b = -100 + 338

Combine like terms: -338 + 338 = 0
0 + -32b = -100 + 338
-32b = -100 + 338

Combine like terms: -100 + 338 = 238
-32b = 238

Divide each side by '-32'.
b = -7.4375

Simplifying
b = -7.4375

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