3f^2(f-3)(f-5)=0

Solution for 3f^2(f-3)(f-5)=0 equation:

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

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

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

Multiply (-3 + f) * (-5 + f)
3f2(-3(-5 + f) + f(-5 + f)) = 0
3f2((-5 * -3 + f * -3) + f(-5 + f)) = 0
3f2((15 + -3f) + f(-5 + f)) = 0
3f2(15 + -3f + (-5 * f + f * f)) = 0
3f2(15 + -3f + (-5f + f2)) = 0

Combine like terms: -3f + -5f = -8f
3f2(15 + -8f + f2) = 0
(15 * 3f2 + -8f * 3f2 + f2 * 3f2) = 0
(45f2 + -24f3 + 3f4) = 0

Solving
45f2 + -24f3 + 3f4 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '3f2'.
3f2(15 + -8f + f2) = 0

Factor a trinomial.
3f2((3 + -1f)(5 + -1f)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'f2' equal to zero and attempt to solve:

Simplifying
f2 = 0

Solving
f2 = 0

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

Simplifying
f2 = 0

Take the square root of each side:
f = {0}
Subproblem 2
Set the factor '(3 + -1f)' equal to zero and attempt to solve:

Simplifying
3 + -1f = 0

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

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

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

Divide each side by '-1'.
f = 3

Simplifying
f = 3
Subproblem 3
Set the factor '(5 + -1f)' equal to zero and attempt to solve:

Simplifying
5 + -1f = 0

Solving
5 + -1f = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1f = 0 + -5
-1f = 0 + -5

Combine like terms: 0 + -5 = -5
-1f = -5

Divide each side by '-1'.
f = 5

Simplifying
f = 5
Solution
f = {0, 3, 5}