7(a+x-b)-8(a-x-b)=-(b-x)

Solution for 7(a+x-b)-8(a-x-b)=-(b-x) equation:

Simplifying
7(a + x + -1b) + -8(a + -1x + -1b) = -1(b + -1x)

Reorder the terms:
7(a + -1b + x) + -8(a + -1x + -1b) = -1(b + -1x)
(a * 7 + -1b * 7 + x * 7) + -8(a + -1x + -1b) = -1(b + -1x)
(7a + -7b + 7x) + -8(a + -1x + -1b) = -1(b + -1x)

Reorder the terms:
7a + -7b + 7x + -8(a + -1b + -1x) = -1(b + -1x)
7a + -7b + 7x + (a * -8 + -1b * -8 + -1x * -8) = -1(b + -1x)
7a + -7b + 7x + (-8a + 8b + 8x) = -1(b + -1x)

Reorder the terms:
7a + -8a + -7b + 8b + 7x + 8x = -1(b + -1x)

Combine like terms: 7a + -8a = -1a
-1a + -7b + 8b + 7x + 8x = -1(b + -1x)

Combine like terms: -7b + 8b = 1b
-1a + 1b + 7x + 8x = -1(b + -1x)

Combine like terms: 7x + 8x = 15x
-1a + 1b + 15x = -1(b + -1x)
-1a + 1b + 15x = (b * -1 + -1x * -1)
-1a + 1b + 15x = (-1b + 1x)

Solving
-1a + 1b + 15x = -1b + 1x

Solving for variable 'a'.

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

Add '-1b' to each side of the equation.
-1a + 1b + -1b + 15x = -1b + -1b + 1x

Combine like terms: 1b + -1b = 0
-1a + 0 + 15x = -1b + -1b + 1x
-1a + 15x = -1b + -1b + 1x

Combine like terms: -1b + -1b = -2b
-1a + 15x = -2b + 1x

Add '-15x' to each side of the equation.
-1a + 15x + -15x = -2b + 1x + -15x

Combine like terms: 15x + -15x = 0
-1a + 0 = -2b + 1x + -15x
-1a = -2b + 1x + -15x

Combine like terms: 1x + -15x = -14x
-1a = -2b + -14x

Divide each side by '-1'.
a = 2b + 14x

Simplifying
a = 2b + 14x