(f+6)(7f+4)=0

Solution for (f+6)(7f+4)=0 equation:

Simplifying
(f + 6)(7f + 4) = 0

Reorder the terms:
(6 + f)(7f + 4) = 0

Reorder the terms:
(6 + f)(4 + 7f) = 0

Multiply (6 + f) * (4 + 7f)
(6(4 + 7f) + f(4 + 7f)) = 0
((4 * 6 + 7f * 6) + f(4 + 7f)) = 0
((24 + 42f) + f(4 + 7f)) = 0
(24 + 42f + (4 * f + 7f * f)) = 0
(24 + 42f + (4f + 7f2)) = 0

Combine like terms: 42f + 4f = 46f
(24 + 46f + 7f2) = 0

Solving
24 + 46f + 7f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(6 + f)(4 + 7f) = 0

Subproblem 1
Set the factor '(6 + f)' equal to zero and attempt to solve:

Simplifying
6 + f = 0

Solving
6 + f = 0

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

Add '-6' to each side of the equation.
6 + -6 + f = 0 + -6

Combine like terms: 6 + -6 = 0
0 + f = 0 + -6
f = 0 + -6

Combine like terms: 0 + -6 = -6
f = -6

Simplifying
f = -6
Subproblem 2
Set the factor '(4 + 7f)' equal to zero and attempt to solve:

Simplifying
4 + 7f = 0

Solving
4 + 7f = 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 + 7f = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7f = 0 + -4
7f = 0 + -4

Combine like terms: 0 + -4 = -4
7f = -4

Divide each side by '7'.
f = -0.5714285714

Simplifying
f = -0.5714285714
Solution
f = {-6, -0.5714285714}