6f^2+48f+42=0

Solution for 6f^2+48f+42=0 equation:

Simplifying
6f2 + 48f + 42 = 0

Reorder the terms:
42 + 48f + 6f2 = 0

Solving
42 + 48f + 6f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '6'.
6(7 + 8f + f2) = 0

Factor a trinomial.
6((7 + f)(1 + f)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(7 + f)' equal to zero and attempt to solve:

Simplifying
7 + f = 0

Solving
7 + f = 0

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

Add '-7' to each side of the equation.
7 + -7 + f = 0 + -7

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

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

Simplifying
f = -7
Subproblem 2
Set the factor '(1 + f)' equal to zero and attempt to solve:

Simplifying
1 + f = 0

Solving
1 + f = 0

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

Add '-1' to each side of the equation.
1 + -1 + f = 0 + -1

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

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

Simplifying
f = -1
Solution
f = {-7, -1}