f^2-3(f+2)-5f^2=

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

Simplifying
f2 + -3(f + 2) + -5f2 = 0

Reorder the terms:
f2 + -3(2 + f) + -5f2 = 0
f2 + (2 * -3 + f * -3) + -5f2 = 0
f2 + (-6 + -3f) + -5f2 = 0

Reorder the terms:
-6 + -3f + f2 + -5f2 = 0

Combine like terms: f2 + -5f2 = -4f2
-6 + -3f + -4f2 = 0

Solving
-6 + -3f + -4f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 3f + 4f2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 3f + 4f2)' equal to zero and attempt to solve:

Simplifying
6 + 3f + 4f2 = 0

Solving
6 + 3f + 4f2 = 0

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

Divide each side by '4'.
1.5 + 0.75f + f2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.75f + -1.5 + f2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.75f + f2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.75f + f2 = 0 + -1.5
0.75f + f2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.75f + f2 = -1.5

The f term is 0.75f.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75f + 0.140625 + f2 = -1.5 + 0.140625

Reorder the terms:
0.140625 + 0.75f + f2 = -1.5 + 0.140625

Combine like terms: -1.5 + 0.140625 = -1.359375
0.140625 + 0.75f + f2 = -1.359375

Factor a perfect square on the left side:
(f + 0.375)(f + 0.375) = -1.359375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.