(-2a+3)(3a-6)=0

Solution for (-2a+3)(3a-6)=0 equation:

Simplifying
(-2a + 3)(3a + -6) = 0

Reorder the terms:
(3 + -2a)(3a + -6) = 0

Reorder the terms:
(3 + -2a)(-6 + 3a) = 0

Multiply (3 + -2a) * (-6 + 3a)
(3(-6 + 3a) + -2a * (-6 + 3a)) = 0
((-6 * 3 + 3a * 3) + -2a * (-6 + 3a)) = 0
((-18 + 9a) + -2a * (-6 + 3a)) = 0
(-18 + 9a + (-6 * -2a + 3a * -2a)) = 0
(-18 + 9a + (12a + -6a2)) = 0

Combine like terms: 9a + 12a = 21a
(-18 + 21a + -6a2) = 0

Solving
-18 + 21a + -6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + 7a + -2a2) = 0

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

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

Simplifying
-2 + a = 0

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

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

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

Simplifying
a = 2
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 = {2, 1.5}