F(x)=2kx^2-x

Solution for F(x)=2kx^2-x equation:

Simplifying
F(x) = 2kx2 + -1x

Multiply F * x
xF = 2kx2 + -1x

Solving
xF = 2kx2 + -1x

Solving for variable 'x'.

Reorder the terms:
-2kx2 + x + xF = 2kx2 + -1x + -2kx2 + x

Reorder the terms:
-2kx2 + x + xF = 2kx2 + -2kx2 + -1x + x

Combine like terms: 2kx2 + -2kx2 = 0
-2kx2 + x + xF = 0 + -1x + x
-2kx2 + x + xF = -1x + x

Combine like terms: -1x + x = 0
-2kx2 + x + xF = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2kx + 1 + F) = 0

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

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-2kx + 1 + F)' equal to zero and attempt to solve:

Simplifying
-2kx + 1 + F = 0

Reorder the terms:
1 + F + -2kx = 0

Solving
1 + F + -2kx = 0

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

Add '-1' to each side of the equation.
1 + F + -1 + -2kx = 0 + -1

Reorder the terms:
1 + -1 + F + -2kx = 0 + -1

Combine like terms: 1 + -1 = 0
0 + F + -2kx = 0 + -1
F + -2kx = 0 + -1

Combine like terms: 0 + -1 = -1
F + -2kx = -1

Add '-1F' to each side of the equation.
F + -1F + -2kx = -1 + -1F

Combine like terms: F + -1F = 0
0 + -2kx = -1 + -1F
-2kx = -1 + -1F

Divide each side by '-2k'.
x = 0.5k-1 + 0.5k-1F

Simplifying
x = 0.5k-1 + 0.5k-1F
Solution
x = {0, 0.5k-1 + 0.5k-1F}