f(a)=a+0.25a(x-2)

Solution for f(a)=a+0.25a(x-2) equation:

Simplifying
f(a) = a + 0.25a(x + -2)

Multiply f * a
af = a + 0.25a(x + -2)

Reorder the terms:
af = a + 0.25a(-2 + x)
af = a + (-2 * 0.25a + x * 0.25a)
af = a + (-0.5a + 0.25ax)

Combine like terms: a + -0.5a = 0.5a
af = 0.5a + 0.25ax

Solving
af = 0.5a + 0.25ax

Solving for variable 'a'.

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

Add '-0.5a' to each side of the equation.
-0.5a + af = 0.5a + -0.5a + 0.25ax

Combine like terms: 0.5a + -0.5a = 0.0
-0.5a + af = 0.0 + 0.25ax
-0.5a + af = 0.25ax

Add '-0.25ax' to each side of the equation.
-0.5a + af + -0.25ax = 0.25ax + -0.25ax

Combine like terms: 0.25ax + -0.25ax = 0.00
-0.5a + af + -0.25ax = 0.00

Factor out the Greatest Common Factor (GCF), 'a'.
a(-0.5 + f + -0.25x) = 0.00

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(-0.5 + f + -0.25x)' equal to zero and attempt to solve:

Simplifying
-0.5 + f + -0.25x = 0

Solving
-0.5 + f + -0.25x = 0

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

Add '0.5' to each side of the equation.
-0.5 + f + 0.5 + -0.25x = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + f + -0.25x = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + f + -0.25x = 0 + 0.5
f + -0.25x = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
f + -0.25x = 0.5

Add '-1f' to each side of the equation.
f + -1f + -0.25x = 0.5 + -1f

Combine like terms: f + -1f = 0
0 + -0.25x = 0.5 + -1f
-0.25x = 0.5 + -1f

Add '0.25x' to each side of the equation.
-0.25x + 0.25x = 0.5 + -1f + 0.25x

Combine like terms: -0.25x + 0.25x = 0.00
0.00 = 0.5 + -1f + 0.25x

Simplifying
0.00 = 0.5 + -1f + 0.25x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}