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

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

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

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

Combine like terms: 4a + 6a = 10a
10a + -3a2 = 2(3a + -2)

Reorder the terms:
10a + -3a2 = 2(-2 + 3a)
10a + -3a2 = (-2 * 2 + 3a * 2)
10a + -3a2 = (-4 + 6a)

Solving
10a + -3a2 = -4 + 6a

Solving for variable 'a'.

Reorder the terms:
4 + 10a + -6a + -3a2 = -4 + 6a + 4 + -6a

Combine like terms: 10a + -6a = 4a
4 + 4a + -3a2 = -4 + 6a + 4 + -6a

Reorder the terms:
4 + 4a + -3a2 = -4 + 4 + 6a + -6a

Combine like terms: -4 + 4 = 0
4 + 4a + -3a2 = 0 + 6a + -6a
4 + 4a + -3a2 = 6a + -6a

Combine like terms: 6a + -6a = 0
4 + 4a + -3a2 = 0

Factor a trinomial.
(2 + -1a)(2 + 3a) = 0

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

Simplifying
2 + -1a = 0

Solving
2 + -1a = 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 + -1a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1a = 0 + -2
-1a = 0 + -2

Combine like terms: 0 + -2 = -2
-1a = -2

Divide each side by '-1'.
a = 2

Simplifying
a = 2
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 = {2, -0.6666666667}