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

Solution for (3a-2)(4a-2)=0 equation:

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

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

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

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

Combine like terms: -8a + -6a = -14a
(4 + -14a + 12a2) = 0

Solving
4 + -14a + 12a2 = 0

Solving for variable 'a'.

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

Factor a trinomial.
2((1 + -2a)(2 + -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 '(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
Solution
a = {0.5, 0.6666666667}