2((3+-4c)(3+-1c))=0

Solution for 2((3+-4c)(3+-1c))=0 equation:

Simplifying
2((3 + -4c)(3 + -1c)) = 0

Multiply (3 + -4c) * (3 + -1c)
2((3(3 + -1c) + -4c * (3 + -1c))) = 0
2(((3 * 3 + -1c * 3) + -4c * (3 + -1c))) = 0
2(((9 + -3c) + -4c * (3 + -1c))) = 0
2((9 + -3c + (3 * -4c + -1c * -4c))) = 0
2((9 + -3c + (-12c + 4c2))) = 0

Combine like terms: -3c + -12c = -15c
2((9 + -15c + 4c2)) = 0
(9 * 2 + -15c * 2 + 4c2 * 2) = 0
(18 + -30c + 8c2) = 0

Solving
18 + -30c + 8c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + -15c + 4c2) = 0

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

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

Simplifying
3 + -4c = 0

Solving
3 + -4c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4c = 0 + -3

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

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

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

Simplifying
c = 0.75
Subproblem 2
Set the factor '(3 + -1c)' equal to zero and attempt to solve:

Simplifying
3 + -1c = 0

Solving
3 + -1c = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1c = 0 + -3

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

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

Divide each side by '-1'.
c = 3

Simplifying
c = 3
Solution
c = {0.75, 3}