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

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

Simplifying
(3a + -2)(a + 3) + 2a = 2 + -1a

Reorder the terms:
(-2 + 3a)(a + 3) + 2a = 2 + -1a

Reorder the terms:
(-2 + 3a)(3 + a) + 2a = 2 + -1a

Multiply (-2 + 3a) * (3 + a)
(-2(3 + a) + 3a * (3 + a)) + 2a = 2 + -1a
((3 * -2 + a * -2) + 3a * (3 + a)) + 2a = 2 + -1a
((-6 + -2a) + 3a * (3 + a)) + 2a = 2 + -1a
(-6 + -2a + (3 * 3a + a * 3a)) + 2a = 2 + -1a
(-6 + -2a + (9a + 3a2)) + 2a = 2 + -1a

Combine like terms: -2a + 9a = 7a
(-6 + 7a + 3a2) + 2a = 2 + -1a

Reorder the terms:
-6 + 7a + 2a + 3a2 = 2 + -1a

Combine like terms: 7a + 2a = 9a
-6 + 9a + 3a2 = 2 + -1a

Solving
-6 + 9a + 3a2 = 2 + -1a

Solving for variable 'a'.

Reorder the terms:
-6 + -2 + 9a + a + 3a2 = 2 + -1a + -2 + a

Combine like terms: -6 + -2 = -8
-8 + 9a + a + 3a2 = 2 + -1a + -2 + a

Combine like terms: 9a + a = 10a
-8 + 10a + 3a2 = 2 + -1a + -2 + a

Reorder the terms:
-8 + 10a + 3a2 = 2 + -2 + -1a + a

Combine like terms: 2 + -2 = 0
-8 + 10a + 3a2 = 0 + -1a + a
-8 + 10a + 3a2 = -1a + a

Combine like terms: -1a + a = 0
-8 + 10a + 3a2 = 0

Factor a trinomial.
(-4 + -1a)(2 + -3a) = 0

Subproblem 1
Set the factor '(-4 + -1a)' equal to zero and attempt to solve:

Simplifying
-4 + -1a = 0

Solving
-4 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1a = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1a = 0 + 4
-1a = 0 + 4

Combine like terms: 0 + 4 = 4
-1a = 4

Divide each side by '-1'.
a = -4

Simplifying
a = -4
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 = {-4, 0.6666666667}