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

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

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

Combine like terms: 5f + -3f = 2f
(5 + 3f)(2f) = 0

Remove parenthesis around (2f)
(5 + 3f) * 2f = 0

Reorder the terms for easier multiplication:
2f(5 + 3f) = 0
(5 * 2f + 3f * 2f) = 0
(10f + 6f2) = 0

Solving
10f + 6f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2f'.
2f(5 + 3f) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'f' equal to zero and attempt to solve:

Simplifying
f = 0

Solving
f = 0

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

Simplifying
f = 0
Subproblem 2
Set the factor '(5 + 3f)' equal to zero and attempt to solve:

Simplifying
5 + 3f = 0

Solving
5 + 3f = 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 + 3f = 0 + -5

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

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

Divide each side by '3'.
f = -1.666666667

Simplifying
f = -1.666666667
Solution
f = {0, -1.666666667}