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

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

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

Reorder the terms:
4a(-2 + 3a) = 2(3a + -2)
(-2 * 4a + 3a * 4a) = 2(3a + -2)
(-8a + 12a2) = 2(3a + -2)

Reorder the terms:
-8a + 12a2 = 2(-2 + 3a)
-8a + 12a2 = (-2 * 2 + 3a * 2)
-8a + 12a2 = (-4 + 6a)

Solving
-8a + 12a2 = -4 + 6a

Solving for variable 'a'.

Reorder the terms:
4 + -8a + -6a + 12a2 = -4 + 6a + 4 + -6a

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

Reorder the terms:
4 + -14a + 12a2 = -4 + 4 + 6a + -6a

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

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

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}