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

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

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

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

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

Multiply (2 + 3a) * (-3 + 4a)
(2(-3 + 4a) + 3a * (-3 + 4a)) = 0
((-3 * 2 + 4a * 2) + 3a * (-3 + 4a)) = 0
((-6 + 8a) + 3a * (-3 + 4a)) = 0
(-6 + 8a + (-3 * 3a + 4a * 3a)) = 0
(-6 + 8a + (-9a + 12a2)) = 0

Combine like terms: 8a + -9a = -1a
(-6 + -1a + 12a2) = 0

Solving
-6 + -1a + 12a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-2 + -3a = 0

Solving
-2 + -3a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3a = 0 + 2
-3a = 0 + 2

Combine like terms: 0 + 2 = 2
-3a = 2

Divide each side by '-3'.
a = -0.6666666667

Simplifying
a = -0.6666666667
Subproblem 2
Set the factor '(3 + -4a)' equal to zero and attempt to solve:

Simplifying
3 + -4a = 0

Solving
3 + -4a = 0

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

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

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

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

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

Simplifying
a = 0.75
Solution
a = {-0.6666666667, 0.75}