(2f+1)(6f-5)=0

Solution for (2f+1)(6f-5)=0 equation:

Simplifying
(2f + 1)(6f + -5) = 0

Reorder the terms:
(1 + 2f)(6f + -5) = 0

Reorder the terms:
(1 + 2f)(-5 + 6f) = 0

Multiply (1 + 2f) * (-5 + 6f)
(1(-5 + 6f) + 2f * (-5 + 6f)) = 0
((-5 * 1 + 6f * 1) + 2f * (-5 + 6f)) = 0
((-5 + 6f) + 2f * (-5 + 6f)) = 0
(-5 + 6f + (-5 * 2f + 6f * 2f)) = 0
(-5 + 6f + (-10f + 12f2)) = 0

Combine like terms: 6f + -10f = -4f
(-5 + -4f + 12f2) = 0

Solving
-5 + -4f + 12f2 = 0

Solving for variable 'f'.

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

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

Simplifying
-1 + -2f = 0

Solving
-1 + -2f = 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 + -2f = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2f = 0 + 1
-2f = 0 + 1

Combine like terms: 0 + 1 = 1
-2f = 1

Divide each side by '-2'.
f = -0.5

Simplifying
f = -0.5
Subproblem 2
Set the factor '(5 + -6f)' equal to zero and attempt to solve:

Simplifying
5 + -6f = 0

Solving
5 + -6f = 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 + -6f = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6f = 0 + -5
-6f = 0 + -5

Combine like terms: 0 + -5 = -5
-6f = -5

Divide each side by '-6'.
f = 0.8333333333

Simplifying
f = 0.8333333333
Solution
f = {-0.5, 0.8333333333}