(4f-3)(2f+6)=0

Solution for (4f-3)(2f+6)=0 equation:

Simplifying
(4f + -3)(2f + 6) = 0

Reorder the terms:
(-3 + 4f)(2f + 6) = 0

Reorder the terms:
(-3 + 4f)(6 + 2f) = 0

Multiply (-3 + 4f) * (6 + 2f)
(-3(6 + 2f) + 4f * (6 + 2f)) = 0
((6 * -3 + 2f * -3) + 4f * (6 + 2f)) = 0
((-18 + -6f) + 4f * (6 + 2f)) = 0
(-18 + -6f + (6 * 4f + 2f * 4f)) = 0
(-18 + -6f + (24f + 8f2)) = 0

Combine like terms: -6f + 24f = 18f
(-18 + 18f + 8f2) = 0

Solving
-18 + 18f + 8f2 = 0

Solving for variable 'f'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 9f + 4f2) = 0

Factor a trinomial.
2((-3 + -1f)(3 + -4f)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -4f)' equal to zero and attempt to solve:

Simplifying
3 + -4f = 0

Solving
3 + -4f = 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 + -4f = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4f = 0 + -3
-4f = 0 + -3

Combine like terms: 0 + -3 = -3
-4f = -3

Divide each side by '-4'.
f = 0.75

Simplifying
f = 0.75
Solution
f = {-3, 0.75}