20f^2=21f-4

Solution for 20f^2=21f-4 equation:

Simplifying
20f2 = 21f + -4

Reorder the terms:
20f2 = -4 + 21f

Solving
20f2 = -4 + 21f

Solving for variable 'f'.

Reorder the terms:
4 + -21f + 20f2 = -4 + 21f + 4 + -21f

Reorder the terms:
4 + -21f + 20f2 = -4 + 4 + 21f + -21f

Combine like terms: -4 + 4 = 0
4 + -21f + 20f2 = 0 + 21f + -21f
4 + -21f + 20f2 = 21f + -21f

Combine like terms: 21f + -21f = 0
4 + -21f + 20f2 = 0

Factor a trinomial.
(1 + -4f)(4 + -5f) = 0

Subproblem 1
Set the factor '(1 + -4f)' equal to zero and attempt to solve:

Simplifying
1 + -4f = 0

Solving
1 + -4f = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4f = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4f = 0 + -1
-4f = 0 + -1

Combine like terms: 0 + -1 = -1
-4f = -1

Divide each side by '-4'.
f = 0.25

Simplifying
f = 0.25
Subproblem 2
Set the factor '(4 + -5f)' equal to zero and attempt to solve:

Simplifying
4 + -5f = 0

Solving
4 + -5f = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5f = 0 + -4
-5f = 0 + -4

Combine like terms: 0 + -4 = -4
-5f = -4

Divide each side by '-5'.
f = 0.8

Simplifying
f = 0.8
Solution
f = {0.25, 0.8}