f(8)f(-5)=3(8)f(-5)-2

Solution for f(8)f(-5)=3(8)f(-5)-2 equation:

Simplifying
f(8) * f(-5) = 3(8) * f(-5) + -2

Reorder the terms for easier multiplication:
8 * -5f * f = 3(8) * f(-5) + -2

Multiply 8 * -5
-40f * f = 3(8) * f(-5) + -2

Multiply f * f
-40f2 = 3(8) * f(-5) + -2

Reorder the terms for easier multiplication:
-40f2 = 3 * 8 * -5f + -2

Multiply 3 * 8
-40f2 = 24 * -5f + -2

Multiply 24 * -5
-40f2 = -120f + -2

Reorder the terms:
-40f2 = -2 + -120f

Solving
-40f2 = -2 + -120f

Solving for variable 'f'.

Reorder the terms:
2 + 120f + -40f2 = -2 + -120f + 2 + 120f

Reorder the terms:
2 + 120f + -40f2 = -2 + 2 + -120f + 120f

Combine like terms: -2 + 2 = 0
2 + 120f + -40f2 = 0 + -120f + 120f
2 + 120f + -40f2 = -120f + 120f

Combine like terms: -120f + 120f = 0
2 + 120f + -40f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 60f + -20f2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 60f + -20f2)' equal to zero and attempt to solve:

Simplifying
1 + 60f + -20f2 = 0

Solving
1 + 60f + -20f2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-0.05 + -3f + f2 = 0.0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -3f + 0.05 + f2 = 0.0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -3f + f2 = 0.0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -3f + f2 = 0.0 + 0.05
-3f + f2 = 0.0 + 0.05

Combine like terms: 0.0 + 0.05 = 0.05
-3f + f2 = 0.05

The f term is -3f.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3f + 2.25 + f2 = 0.05 + 2.25

Reorder the terms:
2.25 + -3f + f2 = 0.05 + 2.25

Combine like terms: 0.05 + 2.25 = 2.3
2.25 + -3f + f2 = 2.3

Factor a perfect square on the left side:
(f + -1.5)(f + -1.5) = 2.3

Calculate the square root of the right side: 1.516575089

Break this problem into two subproblems by setting 
(f + -1.5) equal to 1.516575089 and -1.516575089.

Subproblem 1
f + -1.5 = 1.516575089

Simplifying
f + -1.5 = 1.516575089

Reorder the terms:
-1.5 + f = 1.516575089

Solving
-1.5 + f = 1.516575089

Solving for variable 'f'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + f = 1.516575089 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + f = 1.516575089 + 1.5
f = 1.516575089 + 1.5

Combine like terms: 1.516575089 + 1.5 = 3.016575089
f = 3.016575089

Simplifying
f = 3.016575089

Subproblem 2
f + -1.5 = -1.516575089

Simplifying
f + -1.5 = -1.516575089

Reorder the terms:
-1.5 + f = -1.516575089

Solving
-1.5 + f = -1.516575089

Solving for variable 'f'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + f = -1.516575089 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + f = -1.516575089 + 1.5
f = -1.516575089 + 1.5

Combine like terms: -1.516575089 + 1.5 = -0.016575089
f = -0.016575089

Simplifying
f = -0.016575089

Solution
The solution to the problem is based on the solutions
from the subproblems.
f = {3.016575089, -0.016575089}
Solution
f = {3.016575089, -0.016575089}