(3a+1)(4a-4)=

Solution for (3a+1)(4a-4)= equation:

Simplifying
(3a + 1)(4a + -4) = 0

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

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

Multiply (1 + 3a) * (-4 + 4a)
(1(-4 + 4a) + 3a * (-4 + 4a)) = 0
((-4 * 1 + 4a * 1) + 3a * (-4 + 4a)) = 0
((-4 + 4a) + 3a * (-4 + 4a)) = 0
(-4 + 4a + (-4 * 3a + 4a * 3a)) = 0
(-4 + 4a + (-12a + 12a2)) = 0

Combine like terms: 4a + -12a = -8a
(-4 + -8a + 12a2) = 0

Solving
-4 + -8a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -2a + 3a2) = 0

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

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

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 0

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

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

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

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

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

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

Simplifying
1 + -1a = 0

Solving
1 + -1a = 0

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

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

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

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

Divide each side by '-1'.
a = 1

Simplifying
a = 1
Solution
a = {-0.3333333333, 1}