6(2f-1)+3(4-2f)=2(f+1)+2(f+6)

Solution for 6(2f-1)+3(4-2f)=2(f+1)+2(f+6) equation:

Simplifying
6(2f + -1) + 3(4 + -2f) = 2(f + 1) + 2(f + 6)

Reorder the terms:
6(-1 + 2f) + 3(4 + -2f) = 2(f + 1) + 2(f + 6)
(-1 * 6 + 2f * 6) + 3(4 + -2f) = 2(f + 1) + 2(f + 6)
(-6 + 12f) + 3(4 + -2f) = 2(f + 1) + 2(f + 6)
-6 + 12f + (4 * 3 + -2f * 3) = 2(f + 1) + 2(f + 6)
-6 + 12f + (12 + -6f) = 2(f + 1) + 2(f + 6)

Reorder the terms:
-6 + 12 + 12f + -6f = 2(f + 1) + 2(f + 6)

Combine like terms: -6 + 12 = 6
6 + 12f + -6f = 2(f + 1) + 2(f + 6)

Combine like terms: 12f + -6f = 6f
6 + 6f = 2(f + 1) + 2(f + 6)

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

Reorder the terms:
6 + 6f = 2 + 2f + 2(6 + f)
6 + 6f = 2 + 2f + (6 * 2 + f * 2)
6 + 6f = 2 + 2f + (12 + 2f)

Reorder the terms:
6 + 6f = 2 + 12 + 2f + 2f

Combine like terms: 2 + 12 = 14
6 + 6f = 14 + 2f + 2f

Combine like terms: 2f + 2f = 4f
6 + 6f = 14 + 4f

Solving
6 + 6f = 14 + 4f

Solving for variable 'f'.

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

Add '-4f' to each side of the equation.
6 + 6f + -4f = 14 + 4f + -4f

Combine like terms: 6f + -4f = 2f
6 + 2f = 14 + 4f + -4f

Combine like terms: 4f + -4f = 0
6 + 2f = 14 + 0
6 + 2f = 14

Add '-6' to each side of the equation.
6 + -6 + 2f = 14 + -6

Combine like terms: 6 + -6 = 0
0 + 2f = 14 + -6
2f = 14 + -6

Combine like terms: 14 + -6 = 8
2f = 8

Divide each side by '2'.
f = 4

Simplifying
f = 4