(6f)(3f)+f=550

Solution for (6f)(3f)+f=550 equation:

Simplifying
(6f)(3f) + f = 550

Remove parenthesis around (6f)
6f(3f) + f = 550

Remove parenthesis around (3f)
6f * 3f + f = 550

Reorder the terms for easier multiplication:
6 * 3f * f + f = 550

Multiply 6 * 3
18f * f + f = 550

Multiply f * f
18f2 + f = 550

Reorder the terms:
f + 18f2 = 550

Solving
f + 18f2 = 550

Solving for variable 'f'.

Reorder the terms:
-550 + f + 18f2 = 550 + -550

Combine like terms: 550 + -550 = 0
-550 + f + 18f2 = 0

Factor a trinomial.
(-50 + -9f)(11 + -2f) = 0

Subproblem 1
Set the factor '(-50 + -9f)' equal to zero and attempt to solve:

Simplifying
-50 + -9f = 0

Solving
-50 + -9f = 0

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

Add '50' to each side of the equation.
-50 + 50 + -9f = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -9f = 0 + 50
-9f = 0 + 50

Combine like terms: 0 + 50 = 50
-9f = 50

Divide each side by '-9'.
f = -5.555555556

Simplifying
f = -5.555555556
Subproblem 2
Set the factor '(11 + -2f)' equal to zero and attempt to solve:

Simplifying
11 + -2f = 0

Solving
11 + -2f = 0

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

Add '-11' to each side of the equation.
11 + -11 + -2f = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2f = 0 + -11
-2f = 0 + -11

Combine like terms: 0 + -11 = -11
-2f = -11

Divide each side by '-2'.
f = 5.5

Simplifying
f = 5.5
Solution
f = {-5.555555556, 5.5}