1.5(f+4)+2.5(5-f)=15.7

Solution for 1.5(f+4)+2.5(5-f)=15.7 equation:

Simplifying
1.5(f + 4) + 2.5(5 + -1f) = 15.7

Reorder the terms:
1.5(4 + f) + 2.5(5 + -1f) = 15.7
(4 * 1.5 + f * 1.5) + 2.5(5 + -1f) = 15.7
(6 + 1.5f) + 2.5(5 + -1f) = 15.7
6 + 1.5f + (5 * 2.5 + -1f * 2.5) = 15.7
6 + 1.5f + (12.5 + -2.5f) = 15.7

Reorder the terms:
6 + 12.5 + 1.5f + -2.5f = 15.7

Combine like terms: 6 + 12.5 = 18.5
18.5 + 1.5f + -2.5f = 15.7

Combine like terms: 1.5f + -2.5f = -1f
18.5 + -1f = 15.7

Solving
18.5 + -1f = 15.7

Solving for variable 'f'.

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

Add '-18.5' to each side of the equation.
18.5 + -18.5 + -1f = 15.7 + -18.5

Combine like terms: 18.5 + -18.5 = 0.0
0.0 + -1f = 15.7 + -18.5
-1f = 15.7 + -18.5

Combine like terms: 15.7 + -18.5 = -2.8
-1f = -2.8

Divide each side by '-1'.
f = 2.8

Simplifying
f = 2.8