4f^2+14f=60

Solution for 4f^2+14f=60 equation:

Simplifying
4f2 + 14f = 60

Reorder the terms:
14f + 4f2 = 60

Solving
14f + 4f2 = 60

Solving for variable 'f'.

Reorder the terms:
-60 + 14f + 4f2 = 60 + -60

Combine like terms: 60 + -60 = 0
-60 + 14f + 4f2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + 7f + 2f2) = 0

Factor a trinomial.
2((-6 + -1f)(5 + -2f)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1f)' equal to zero and attempt to solve:

Simplifying
-6 + -1f = 0

Solving
-6 + -1f = 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 + -1f = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1f = 0 + 6
-1f = 0 + 6

Combine like terms: 0 + 6 = 6
-1f = 6

Divide each side by '-1'.
f = -6

Simplifying
f = -6
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 = {-6, 2.5}