(3c+1)(4c+4)=

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

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

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

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

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

Combine like terms: 4c + 12c = 16c
(4 + 16c + 12c2) = 0

Solving
4 + 16c + 12c2 = 0

Solving for variable 'c'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4c + 3c2) = 0

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

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

Simplifying
1 + c = 0

Solving
1 + c = 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 + c = 0 + -1

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

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

Simplifying
c = -1
Subproblem 2
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
Solution
c = {-1, -0.3333333333}