(3a-4)(4a+2)=

Solution for (3a-4)(4a+2)= equation:

Simplifying
(3a + -4)(4a + 2) = 0

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

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

Multiply (-4 + 3a) * (2 + 4a)
(-4(2 + 4a) + 3a * (2 + 4a)) = 0
((2 * -4 + 4a * -4) + 3a * (2 + 4a)) = 0
((-8 + -16a) + 3a * (2 + 4a)) = 0
(-8 + -16a + (2 * 3a + 4a * 3a)) = 0
(-8 + -16a + (6a + 12a2)) = 0

Combine like terms: -16a + 6a = -10a
(-8 + -10a + 12a2) = 0

Solving
-8 + -10a + 12a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -5a + 6a2) = 0

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

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

Simplifying
-1 + -2a = 0

Solving
-1 + -2a = 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 + -2a = 0 + 1

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

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

Divide each side by '-2'.
a = -0.5

Simplifying
a = -0.5
Subproblem 2
Set the factor '(4 + -3a)' equal to zero and attempt to solve:

Simplifying
4 + -3a = 0

Solving
4 + -3a = 0

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

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

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

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

Divide each side by '-3'.
a = 1.333333333

Simplifying
a = 1.333333333
Solution
a = {-0.5, 1.333333333}