6f^2+5f-6=0

Solution for 6f^2+5f-6=0 equation:

Simplifying
6f2 + 5f + -6 = 0

Reorder the terms:
-6 + 5f + 6f2 = 0

Solving
-6 + 5f + 6f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-3 + -2f)(2 + -3f) = 0

Subproblem 1
Set the factor '(-3 + -2f)' equal to zero and attempt to solve:

Simplifying
-3 + -2f = 0

Solving
-3 + -2f = 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 + -2f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2f = 0 + 3
-2f = 0 + 3

Combine like terms: 0 + 3 = 3
-2f = 3

Divide each side by '-2'.
f = -1.5

Simplifying
f = -1.5
Subproblem 2
Set the factor '(2 + -3f)' equal to zero and attempt to solve:

Simplifying
2 + -3f = 0

Solving
2 + -3f = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3f = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3f = 0 + -2
-3f = 0 + -2

Combine like terms: 0 + -2 = -2
-3f = -2

Divide each side by '-3'.
f = 0.6666666667

Simplifying
f = 0.6666666667
Solution
f = {-1.5, 0.6666666667}