9f^2-12f=5

Solution for 9f^2-12f=5 equation:

Simplifying
9f2 + -12f = 5

Reorder the terms:
-12f + 9f2 = 5

Solving
-12f + 9f2 = 5

Solving for variable 'f'.

Reorder the terms:
-5 + -12f + 9f2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -12f + 9f2 = 0

Factor a trinomial.
(-1 + -3f)(5 + -3f) = 0

Subproblem 1
Set the factor '(-1 + -3f)' equal to zero and attempt to solve:

Simplifying
-1 + -3f = 0

Solving
-1 + -3f = 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 + -3f = 0 + 1

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

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

Divide each side by '-3'.
f = -0.3333333333

Simplifying
f = -0.3333333333
Subproblem 2
Set the factor '(5 + -3f)' equal to zero and attempt to solve:

Simplifying
5 + -3f = 0

Solving
5 + -3f = 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 + -3f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3f = 0 + -5
-3f = 0 + -5

Combine like terms: 0 + -5 = -5
-3f = -5

Divide each side by '-3'.
f = 1.666666667

Simplifying
f = 1.666666667
Solution
f = {-0.3333333333, 1.666666667}