(4-2b)-(5-3b)=(b-1)-(b-8)

Solution for (4-2b)-(5-3b)=(b-1)-(b-8) equation:

Simplifying
(4 + -2b) + -1(5 + -3b) = (b + -1) + -1(b + -8)

Remove parenthesis around (4 + -2b)
4 + -2b + -1(5 + -3b) = (b + -1) + -1(b + -8)
4 + -2b + (5 * -1 + -3b * -1) = (b + -1) + -1(b + -8)
4 + -2b + (-5 + 3b) = (b + -1) + -1(b + -8)

Reorder the terms:
4 + -5 + -2b + 3b = (b + -1) + -1(b + -8)

Combine like terms: 4 + -5 = -1
-1 + -2b + 3b = (b + -1) + -1(b + -8)

Combine like terms: -2b + 3b = 1b
-1 + 1b = (b + -1) + -1(b + -8)

Reorder the terms:
-1 + 1b = (-1 + b) + -1(b + -8)

Remove parenthesis around (-1 + b)
-1 + 1b = -1 + b + -1(b + -8)

Reorder the terms:
-1 + 1b = -1 + b + -1(-8 + b)
-1 + 1b = -1 + b + (-8 * -1 + b * -1)
-1 + 1b = -1 + b + (8 + -1b)

Reorder the terms:
-1 + 1b = -1 + 8 + b + -1b

Combine like terms: -1 + 8 = 7
-1 + 1b = 7 + b + -1b

Combine like terms: b + -1b = 0
-1 + 1b = 7 + 0
-1 + 1b = 7

Solving
-1 + 1b = 7

Solving for variable 'b'.

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

Add '1' to each side of the equation.
-1 + 1 + 1b = 7 + 1

Combine like terms: -1 + 1 = 0
0 + 1b = 7 + 1
1b = 7 + 1

Combine like terms: 7 + 1 = 8
1b = 8

Divide each side by '1'.
b = 8

Simplifying
b = 8