6(1-7b)+7(b-3)=55

Solution for 6(1-7b)+7(b-3)=55 equation:

Simplifying
6(1 + -7b) + 7(b + -3) = 55
(1 * 6 + -7b * 6) + 7(b + -3) = 55
(6 + -42b) + 7(b + -3) = 55

Reorder the terms:
6 + -42b + 7(-3 + b) = 55
6 + -42b + (-3 * 7 + b * 7) = 55
6 + -42b + (-21 + 7b) = 55

Reorder the terms:
6 + -21 + -42b + 7b = 55

Combine like terms: 6 + -21 = -15
-15 + -42b + 7b = 55

Combine like terms: -42b + 7b = -35b
-15 + -35b = 55

Solving
-15 + -35b = 55

Solving for variable 'b'.

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

Add '15' to each side of the equation.
-15 + 15 + -35b = 55 + 15

Combine like terms: -15 + 15 = 0
0 + -35b = 55 + 15
-35b = 55 + 15

Combine like terms: 55 + 15 = 70
-35b = 70

Divide each side by '-35'.
b = -2

Simplifying
b = -2