51-(4c+1)=5(c+2)+c

Solution for 51-(4c+1)=5(c+2)+c equation:

Simplifying
51 + -1(4c + 1) = 5(c + 2) + c

Reorder the terms:
51 + -1(1 + 4c) = 5(c + 2) + c
51 + (1 * -1 + 4c * -1) = 5(c + 2) + c
51 + (-1 + -4c) = 5(c + 2) + c

Combine like terms: 51 + -1 = 50
50 + -4c = 5(c + 2) + c

Reorder the terms:
50 + -4c = 5(2 + c) + c
50 + -4c = (2 * 5 + c * 5) + c
50 + -4c = (10 + 5c) + c

Combine like terms: 5c + c = 6c
50 + -4c = 10 + 6c

Solving
50 + -4c = 10 + 6c

Solving for variable 'c'.

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

Add '-6c' to each side of the equation.
50 + -4c + -6c = 10 + 6c + -6c

Combine like terms: -4c + -6c = -10c
50 + -10c = 10 + 6c + -6c

Combine like terms: 6c + -6c = 0
50 + -10c = 10 + 0
50 + -10c = 10

Add '-50' to each side of the equation.
50 + -50 + -10c = 10 + -50

Combine like terms: 50 + -50 = 0
0 + -10c = 10 + -50
-10c = 10 + -50

Combine like terms: 10 + -50 = -40
-10c = -40

Divide each side by '-10'.
c = 4

Simplifying
c = 4