10y^2-y=f(y)

Solution for 10y^2-y=f(y) equation:

Simplifying
10y2 + -1y = f(y)

Reorder the terms:
-1y + 10y2 = f(y)

Multiply f * y
-1y + 10y2 = fy

Solving
-1y + 10y2 = fy

Solving for variable 'y'.

Reorder the terms:
-1fy + -1y + 10y2 = fy + -1fy

Combine like terms: fy + -1fy = 0
-1fy + -1y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), 'y'.
y(-1f + -1 + 10y) = 0

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

Simplifying
y = 0

Solving
y = 0

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

Simplifying
y = 0
Subproblem 2
Set the factor '(-1f + -1 + 10y)' equal to zero and attempt to solve:

Simplifying
-1f + -1 + 10y = 0

Reorder the terms:
-1 + -1f + 10y = 0

Solving
-1 + -1f + 10y = 0

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

Add '1' to each side of the equation.
-1 + -1f + 1 + 10y = 0 + 1

Reorder the terms:
-1 + 1 + -1f + 10y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1f + 10y = 0 + 1
-1f + 10y = 0 + 1

Combine like terms: 0 + 1 = 1
-1f + 10y = 1

Add 'f' to each side of the equation.
-1f + f + 10y = 1 + f

Combine like terms: -1f + f = 0
0 + 10y = 1 + f
10y = 1 + f

Divide each side by '10'.
y = 0.1 + 0.1f

Simplifying
y = 0.1 + 0.1f
Solution
y = {0, 0.1 + 0.1f}