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

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

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

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

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

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

Combine like terms: -9a + 4a = -5a
(-6 + -5a + 6a2) = 0

Solving
-6 + -5a + 6a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -3a)(3 + -2a) = 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 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

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

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

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-0.6666666667, 1.5}