(f+4)(2f-5)=0

Solution for (f+4)(2f-5)=0 equation:

Simplifying
(f + 4)(2f + -5) = 0

Reorder the terms:
(4 + f)(2f + -5) = 0

Reorder the terms:
(4 + f)(-5 + 2f) = 0

Multiply (4 + f) * (-5 + 2f)
(4(-5 + 2f) + f(-5 + 2f)) = 0
((-5 * 4 + 2f * 4) + f(-5 + 2f)) = 0
((-20 + 8f) + f(-5 + 2f)) = 0
(-20 + 8f + (-5 * f + 2f * f)) = 0
(-20 + 8f + (-5f + 2f2)) = 0

Combine like terms: 8f + -5f = 3f
(-20 + 3f + 2f2) = 0

Solving
-20 + 3f + 2f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-4 + -1f)(5 + -2f) = 0

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

Simplifying
-4 + -1f = 0

Solving
-4 + -1f = 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 + -1f = 0 + 4

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

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

Divide each side by '-1'.
f = -4

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

Simplifying
5 + -2f = 0

Solving
5 + -2f = 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 + -2f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2f = 0 + -5
-2f = 0 + -5

Combine like terms: 0 + -5 = -5
-2f = -5

Divide each side by '-2'.
f = 2.5

Simplifying
f = 2.5
Solution
f = {-4, 2.5}