2(3f+1)+f=3f+5f-2(f-1)

Solution for 2(3f+1)+f=3f+5f-2(f-1) equation:

Simplifying
2(3f + 1) + f = 3f + 5f + -2(f + -1)

Reorder the terms:
2(1 + 3f) + f = 3f + 5f + -2(f + -1)
(1 * 2 + 3f * 2) + f = 3f + 5f + -2(f + -1)
(2 + 6f) + f = 3f + 5f + -2(f + -1)

Combine like terms: 6f + f = 7f
2 + 7f = 3f + 5f + -2(f + -1)

Reorder the terms:
2 + 7f = 3f + 5f + -2(-1 + f)
2 + 7f = 3f + 5f + (-1 * -2 + f * -2)
2 + 7f = 3f + 5f + (2 + -2f)

Reorder the terms:
2 + 7f = 2 + 3f + 5f + -2f

Combine like terms: 3f + 5f = 8f
2 + 7f = 2 + 8f + -2f

Combine like terms: 8f + -2f = 6f
2 + 7f = 2 + 6f

Add '-2' to each side of the equation.
2 + -2 + 7f = 2 + -2 + 6f

Combine like terms: 2 + -2 = 0
0 + 7f = 2 + -2 + 6f
7f = 2 + -2 + 6f

Combine like terms: 2 + -2 = 0
7f = 0 + 6f
7f = 6f

Solving
7f = 6f

Solving for variable 'f'.

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

Add '-6f' to each side of the equation.
7f + -6f = 6f + -6f

Combine like terms: 7f + -6f = 1f
1f = 6f + -6f

Combine like terms: 6f + -6f = 0
1f = 0

Divide each side by '1'.
f = 0

Simplifying
f = 0