(f-5)(2f+9)=0

Solution for (f-5)(2f+9)=0 equation:

Simplifying
(f + -5)(2f + 9) = 0

Reorder the terms:
(-5 + f)(2f + 9) = 0

Reorder the terms:
(-5 + f)(9 + 2f) = 0

Multiply (-5 + f) * (9 + 2f)
(-5(9 + 2f) + f(9 + 2f)) = 0
((9 * -5 + 2f * -5) + f(9 + 2f)) = 0
((-45 + -10f) + f(9 + 2f)) = 0
(-45 + -10f + (9 * f + 2f * f)) = 0
(-45 + -10f + (9f + 2f2)) = 0

Combine like terms: -10f + 9f = -1f
(-45 + -1f + 2f2) = 0

Solving
-45 + -1f + 2f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-9 + -2f)(5 + -1f) = 0

Subproblem 1
Set the factor '(-9 + -2f)' equal to zero and attempt to solve:

Simplifying
-9 + -2f = 0

Solving
-9 + -2f = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2f = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2f = 0 + 9
-2f = 0 + 9

Combine like terms: 0 + 9 = 9
-2f = 9

Divide each side by '-2'.
f = -4.5

Simplifying
f = -4.5
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 = {-4.5, 5}