.10=(F(.05)+(1-f))((.6*.14)+(.4*.10))

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Solution for .10=(F(.05)+(1-f))((.6*.14)+(.4*.10)) equation: 


Simplifying
0.10 = (F(0.05) + (1 + -1f))((0.6 * 0.14) + (0.4 * 0.10))

Reorder the terms for easier multiplication:
0.10 = (0.05F + (1 + -1f))((0.6 * 0.14) + (0.4 * 0.10))

Remove parenthesis around (1 + -1f)
0.10 = (0.05F + 1 + -1f)((0.6 * 0.14) + (0.4 * 0.10))

Reorder the terms:
0.10 = (1 + 0.05F + -1f)((0.6 * 0.14) + (0.4 * 0.10))

Multiply 0.6 * 0.14
0.10 = (1 + 0.05F + -1f)((0.084) + (0.4 * 0.10))
0.10 = (1 + 0.05F + -1f)(0.084 + (0.4 * 0.10))

Multiply 0.4 * 0.10
0.10 = (1 + 0.05F + -1f)(0.084 + (0.04))
0.10 = (1 + 0.05F + -1f)(0.084 + 0.04)

Combine like terms: 0.084 + 0.04 = 0.124
0.10 = (1 + 0.05F + -1f)(0.124)

Reorder the terms for easier multiplication:
0.10 = 0.124(1 + 0.05F + -1f)
0.10 = (1 * 0.124 + 0.05F * 0.124 + -1f * 0.124)
0.10 = (0.124 + 0.0062F + -0.124f)

Solving
0.10 = 0.124 + 0.0062F + -0.124f

Solving for variable 'F'.

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

Add '-0.0062F' to each side of the equation.
0.10 + -0.0062F = 0.124 + 0.0062F + -0.0062F + -0.124f

Combine like terms: 0.0062F + -0.0062F = 0.0000
0.10 + -0.0062F = 0.124 + 0.0000 + -0.124f
0.10 + -0.0062F = 0.124 + -0.124f

Add '-0.10' to each side of the equation.
0.10 + -0.10 + -0.0062F = 0.124 + -0.10 + -0.124f

Combine like terms: 0.10 + -0.10 = 0.00
0.00 + -0.0062F = 0.124 + -0.10 + -0.124f
-0.0062F = 0.124 + -0.10 + -0.124f

Combine like terms: 0.124 + -0.10 = 0.024
-0.0062F = 0.024 + -0.124f

Divide each side by '-0.0062'.
F = -3.870967742 + 20f

Simplifying
F = -3.870967742 + 20f

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