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

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

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

Reorder the terms:
(1 + 3c)(2c + -4) = 0

Reorder the terms:
(1 + 3c)(-4 + 2c) = 0

Multiply (1 + 3c) * (-4 + 2c)
(1(-4 + 2c) + 3c * (-4 + 2c)) = 0
((-4 * 1 + 2c * 1) + 3c * (-4 + 2c)) = 0
((-4 + 2c) + 3c * (-4 + 2c)) = 0
(-4 + 2c + (-4 * 3c + 2c * 3c)) = 0
(-4 + 2c + (-12c + 6c2)) = 0

Combine like terms: 2c + -12c = -10c
(-4 + -10c + 6c2) = 0

Solving
-4 + -10c + 6c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -5c + 3c2) = 0

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

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

Simplifying
-1 + -3c = 0

Solving
-1 + -3c = 0

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

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

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

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

Divide each side by '-3'.
c = -0.3333333333

Simplifying
c = -0.3333333333
Subproblem 2
Set the factor '(2 + -1c)' equal to zero and attempt to solve:

Simplifying
2 + -1c = 0

Solving
2 + -1c = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1c = 0 + -2

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

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

Divide each side by '-1'.
c = 2

Simplifying
c = 2
Solution
c = {-0.3333333333, 2}