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

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


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

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

Reorder the terms:
-329 + -9 + 49q = 9[7(9q + -8) + 6] + -82

Combine like terms: -329 + -9 = -338
-338 + 49q = 9[7(9q + -8) + 6] + -82

Reorder the terms:
-338 + 49q = 9[7(-8 + 9q) + 6] + -82
-338 + 49q = 9[(-8 * 7 + 9q * 7) + 6] + -82
-338 + 49q = 9[(-56 + 63q) + 6] + -82

Reorder the terms:
-338 + 49q = 9[-56 + 6 + 63q] + -82

Combine like terms: -56 + 6 = -50
-338 + 49q = 9[-50 + 63q] + -82
-338 + 49q = [-50 * 9 + 63q * 9] + -82
-338 + 49q = [-450 + 567q] + -82

Reorder the terms:
-338 + 49q = -450 + -82 + 567q

Combine like terms: -450 + -82 = -532
-338 + 49q = -532 + 567q

Solving
-338 + 49q = -532 + 567q

Solving for variable 'q'.

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

Add '-567q' to each side of the equation.
-338 + 49q + -567q = -532 + 567q + -567q

Combine like terms: 49q + -567q = -518q
-338 + -518q = -532 + 567q + -567q

Combine like terms: 567q + -567q = 0
-338 + -518q = -532 + 0
-338 + -518q = -532

Add '338' to each side of the equation.
-338 + 338 + -518q = -532 + 338

Combine like terms: -338 + 338 = 0
0 + -518q = -532 + 338
-518q = -532 + 338

Combine like terms: -532 + 338 = -194
-518q = -194

Divide each side by '-518'.
q = 0.3745173745

Simplifying
q = 0.3745173745

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