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

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

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

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

Reorder the terms:
6 + 4a + -3a = 2a(3a + -2)

Combine like terms: 4a + -3a = 1a
6 + 1a = 2a(3a + -2)

Reorder the terms:
6 + 1a = 2a(-2 + 3a)
6 + 1a = (-2 * 2a + 3a * 2a)
6 + 1a = (-4a + 6a2)

Solving
6 + 1a = -4a + 6a2

Solving for variable 'a'.

Combine like terms: 1a + 4a = 5a
6 + 5a + -6a2 = -4a + 6a2 + 4a + -6a2

Reorder the terms:
6 + 5a + -6a2 = -4a + 4a + 6a2 + -6a2

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

Combine like terms: 6a2 + -6a2 = 0
6 + 5a + -6a2 = 0

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

Subproblem 1
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
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 = {1.5, -0.6666666667}