(f-5)(3f+8)=0

Solution for (f-5)(3f+8)=0 equation:

Simplifying
(f + -5)(3f + 8) = 0

Reorder the terms:
(-5 + f)(3f + 8) = 0

Reorder the terms:
(-5 + f)(8 + 3f) = 0

Multiply (-5 + f) * (8 + 3f)
(-5(8 + 3f) + f(8 + 3f)) = 0
((8 * -5 + 3f * -5) + f(8 + 3f)) = 0
((-40 + -15f) + f(8 + 3f)) = 0
(-40 + -15f + (8 * f + 3f * f)) = 0
(-40 + -15f + (8f + 3f2)) = 0

Combine like terms: -15f + 8f = -7f
(-40 + -7f + 3f2) = 0

Solving
-40 + -7f + 3f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-8 + -3f)(5 + -1f) = 0

Subproblem 1
Set the factor '(-8 + -3f)' equal to zero and attempt to solve:

Simplifying
-8 + -3f = 0

Solving
-8 + -3f = 0

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

Add '8' to each side of the equation.
-8 + 8 + -3f = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -3f = 0 + 8
-3f = 0 + 8

Combine like terms: 0 + 8 = 8
-3f = 8

Divide each side by '-3'.
f = -2.666666667

Simplifying
f = -2.666666667
Subproblem 2
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 = {-2.666666667, 5}