45f^2+27f-72=0

Solution for 45f^2+27f-72=0 equation:

Simplifying
45f2 + 27f + -72 = 0

Reorder the terms:
-72 + 27f + 45f2 = 0

Solving
-72 + 27f + 45f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-8 + 3f + 5f2) = 0

Factor a trinomial.
9((-8 + -5f)(1 + -1f)) = 0

Ignore the factor 9.
Subproblem 1
Set the factor '(-8 + -5f)' equal to zero and attempt to solve:

Simplifying
-8 + -5f = 0

Solving
-8 + -5f = 0

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

Add '8' to each side of the equation.
-8 + 8 + -5f = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -5f = 0 + 8
-5f = 0 + 8

Combine like terms: 0 + 8 = 8
-5f = 8

Divide each side by '-5'.
f = -1.6

Simplifying
f = -1.6
Subproblem 2
Set the factor '(1 + -1f)' equal to zero and attempt to solve:

Simplifying
1 + -1f = 0

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

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

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

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

Simplifying
f = 1
Solution
f = {-1.6, 1}