6[5-7(x-1)]+5[(5x+7)-9]=15x-338

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Solution for 6[5-7(x-1)]+5[(5x+7)-9]=15x-338 equation: 


Simplifying
6[5 + -7(x + -1)] + 5[(5x + 7) + -9] = 15x + -338

Reorder the terms:
6[5 + -7(-1 + x)] + 5[(5x + 7) + -9] = 15x + -338
6[5 + (-1 * -7 + x * -7)] + 5[(5x + 7) + -9] = 15x + -338
6[5 + (7 + -7x)] + 5[(5x + 7) + -9] = 15x + -338

Combine like terms: 5 + 7 = 12
6[12 + -7x] + 5[(5x + 7) + -9] = 15x + -338
[12 * 6 + -7x * 6] + 5[(5x + 7) + -9] = 15x + -338
[72 + -42x] + 5[(5x + 7) + -9] = 15x + -338

Reorder the terms:
72 + -42x + 5[(7 + 5x) + -9] = 15x + -338

Remove parenthesis around (7 + 5x)
72 + -42x + 5[7 + 5x + -9] = 15x + -338

Reorder the terms:
72 + -42x + 5[7 + -9 + 5x] = 15x + -338

Combine like terms: 7 + -9 = -2
72 + -42x + 5[-2 + 5x] = 15x + -338
72 + -42x + [-2 * 5 + 5x * 5] = 15x + -338
72 + -42x + [-10 + 25x] = 15x + -338

Reorder the terms:
72 + -10 + -42x + 25x = 15x + -338

Combine like terms: 72 + -10 = 62
62 + -42x + 25x = 15x + -338

Combine like terms: -42x + 25x = -17x
62 + -17x = 15x + -338

Reorder the terms:
62 + -17x = -338 + 15x

Solving
62 + -17x = -338 + 15x

Solving for variable 'x'.

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

Add '-15x' to each side of the equation.
62 + -17x + -15x = -338 + 15x + -15x

Combine like terms: -17x + -15x = -32x
62 + -32x = -338 + 15x + -15x

Combine like terms: 15x + -15x = 0
62 + -32x = -338 + 0
62 + -32x = -338

Add '-62' to each side of the equation.
62 + -62 + -32x = -338 + -62

Combine like terms: 62 + -62 = 0
0 + -32x = -338 + -62
-32x = -338 + -62

Combine like terms: -338 + -62 = -400
-32x = -400

Divide each side by '-32'.
x = 12.5

Simplifying
x = 12.5

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