15f^2-4f-3=0

Solution for 15f^2-4f-3=0 equation:

Simplifying
15f2 + -4f + -3 = 0

Reorder the terms:
-3 + -4f + 15f2 = 0

Solving
-3 + -4f + 15f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-1 + -3f)(3 + -5f) = 0

Subproblem 1
Set the factor '(-1 + -3f)' equal to zero and attempt to solve:

Simplifying
-1 + -3f = 0

Solving
-1 + -3f = 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 + -3f = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3f = 0 + 1
-3f = 0 + 1

Combine like terms: 0 + 1 = 1
-3f = 1

Divide each side by '-3'.
f = -0.3333333333

Simplifying
f = -0.3333333333
Subproblem 2
Set the factor '(3 + -5f)' equal to zero and attempt to solve:

Simplifying
3 + -5f = 0

Solving
3 + -5f = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5f = 0 + -3
-5f = 0 + -3

Combine like terms: 0 + -3 = -3
-5f = -3

Divide each side by '-5'.
f = 0.6

Simplifying
f = 0.6
Solution
f = {-0.3333333333, 0.6}