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

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

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

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

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

Combine like terms: -2 + 12 = 10
10 + 4f + -6f = 2(f + 1) + 2(f + 6)

Combine like terms: 4f + -6f = -2f
10 + -2f = 2(f + 1) + 2(f + 6)

Reorder the terms:
10 + -2f = 2(1 + f) + 2(f + 6)
10 + -2f = (1 * 2 + f * 2) + 2(f + 6)
10 + -2f = (2 + 2f) + 2(f + 6)

Reorder the terms:
10 + -2f = 2 + 2f + 2(6 + f)
10 + -2f = 2 + 2f + (6 * 2 + f * 2)
10 + -2f = 2 + 2f + (12 + 2f)

Reorder the terms:
10 + -2f = 2 + 12 + 2f + 2f

Combine like terms: 2 + 12 = 14
10 + -2f = 14 + 2f + 2f

Combine like terms: 2f + 2f = 4f
10 + -2f = 14 + 4f

Solving
10 + -2f = 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.
10 + -2f + -4f = 14 + 4f + -4f

Combine like terms: -2f + -4f = -6f
10 + -6f = 14 + 4f + -4f

Combine like terms: 4f + -4f = 0
10 + -6f = 14 + 0
10 + -6f = 14

Add '-10' to each side of the equation.
10 + -10 + -6f = 14 + -10

Combine like terms: 10 + -10 = 0
0 + -6f = 14 + -10
-6f = 14 + -10

Combine like terms: 14 + -10 = 4
-6f = 4

Divide each side by '-6'.
f = -0.6666666667

Simplifying
f = -0.6666666667