50-(b+c)+50(a+c)=50-(a+b)

Solution for 50-(b+c)+50(a+c)=50-(a+b) equation:

Simplifying
50 + -1(b + c) + 50(a + c) = 50 + -1(a + b)
50 + (b * -1 + c * -1) + 50(a + c) = 50 + -1(a + b)
50 + (-1b + -1c) + 50(a + c) = 50 + -1(a + b)
50 + -1b + -1c + (a * 50 + c * 50) = 50 + -1(a + b)
50 + -1b + -1c + (50a + 50c) = 50 + -1(a + b)

Reorder the terms:
50 + 50a + -1b + -1c + 50c = 50 + -1(a + b)

Combine like terms: -1c + 50c = 49c
50 + 50a + -1b + 49c = 50 + -1(a + b)
50 + 50a + -1b + 49c = 50 + (a * -1 + b * -1)
50 + 50a + -1b + 49c = 50 + (-1a + -1b)

Add '-50' to each side of the equation.
50 + 50a + -1b + -50 + 49c = 50 + -1a + -50 + -1b

Reorder the terms:
50 + -50 + 50a + -1b + 49c = 50 + -1a + -50 + -1b

Combine like terms: 50 + -50 = 0
0 + 50a + -1b + 49c = 50 + -1a + -50 + -1b
50a + -1b + 49c = 50 + -1a + -50 + -1b

Reorder the terms:
50a + -1b + 49c = 50 + -50 + -1a + -1b

Combine like terms: 50 + -50 = 0
50a + -1b + 49c = 0 + -1a + -1b
50a + -1b + 49c = -1a + -1b

Add 'b' to each side of the equation.
50a + -1b + b + 49c = -1a + -1b + b

Combine like terms: -1b + b = 0
50a + 0 + 49c = -1a + -1b + b
50a + 49c = -1a + -1b + b

Combine like terms: -1b + b = 0
50a + 49c = -1a + 0
50a + 49c = -1a

Solving
50a + 49c = -1a

Solving for variable 'a'.

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

Add 'a' to each side of the equation.
50a + a + 49c = -1a + a

Combine like terms: 50a + a = 51a
51a + 49c = -1a + a

Combine like terms: -1a + a = 0
51a + 49c = 0

Add '-49c' to each side of the equation.
51a + 49c + -49c = 0 + -49c

Combine like terms: 49c + -49c = 0
51a + 0 = 0 + -49c
51a = 0 + -49c
Remove the zero:
51a = -49c

Divide each side by '51'.
a = -0.9607843137c

Simplifying
a = -0.9607843137c