24f=144-8f^2

Solution for 24f=144-8f^2 equation:

Simplifying
24f = 144 + -8f2

Solving
24f = 144 + -8f2

Solving for variable 'f'.

Reorder the terms:
-144 + 24f + 8f2 = 144 + -8f2 + -144 + 8f2

Reorder the terms:
-144 + 24f + 8f2 = 144 + -144 + -8f2 + 8f2

Combine like terms: 144 + -144 = 0
-144 + 24f + 8f2 = 0 + -8f2 + 8f2
-144 + 24f + 8f2 = -8f2 + 8f2

Combine like terms: -8f2 + 8f2 = 0
-144 + 24f + 8f2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-18 + 3f + f2) = 0

Factor a trinomial.
8((-6 + -1f)(3 + -1f)) = 0

Ignore the factor 8.
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 '(3 + -1f)' equal to zero and attempt to solve:

Simplifying
3 + -1f = 0

Solving
3 + -1f = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1f = 0 + -3
-1f = 0 + -3

Combine like terms: 0 + -3 = -3
-1f = -3

Divide each side by '-1'.
f = 3

Simplifying
f = 3
Solution
f = {-6, 3}