(2f-6)(6f-7)=0

Solution for (2f-6)(6f-7)=0 equation:

Simplifying
(2f + -6)(6f + -7) = 0

Reorder the terms:
(-6 + 2f)(6f + -7) = 0

Reorder the terms:
(-6 + 2f)(-7 + 6f) = 0

Multiply (-6 + 2f) * (-7 + 6f)
(-6(-7 + 6f) + 2f * (-7 + 6f)) = 0
((-7 * -6 + 6f * -6) + 2f * (-7 + 6f)) = 0
((42 + -36f) + 2f * (-7 + 6f)) = 0
(42 + -36f + (-7 * 2f + 6f * 2f)) = 0
(42 + -36f + (-14f + 12f2)) = 0

Combine like terms: -36f + -14f = -50f
(42 + -50f + 12f2) = 0

Solving
42 + -50f + 12f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + -25f + 6f2) = 0

Factor a trinomial.
2((7 + -6f)(3 + -1f)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + -6f)' equal to zero and attempt to solve:

Simplifying
7 + -6f = 0

Solving
7 + -6f = 0

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

Add '-7' to each side of the equation.
7 + -7 + -6f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6f = 0 + -7
-6f = 0 + -7

Combine like terms: 0 + -7 = -7
-6f = -7

Divide each side by '-6'.
f = 1.166666667

Simplifying
f = 1.166666667
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 = {1.166666667, 3}