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

Solution for a(3a+1)+2(a-3)= equation:

Simplifying
a(3a + 1) + 2(a + -3) = 0

Reorder the terms:
a(1 + 3a) + 2(a + -3) = 0
(1 * a + 3a * a) + 2(a + -3) = 0
(1a + 3a2) + 2(a + -3) = 0

Reorder the terms:
1a + 3a2 + 2(-3 + a) = 0
1a + 3a2 + (-3 * 2 + a * 2) = 0
1a + 3a2 + (-6 + 2a) = 0

Reorder the terms:
-6 + 1a + 2a + 3a2 = 0

Combine like terms: 1a + 2a = 3a
-6 + 3a + 3a2 = 0

Solving
-6 + 3a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-2 + a + a2) = 0

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

Ignore the factor 3.
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 '(1 + -1a)' equal to zero and attempt to solve:

Simplifying
1 + -1a = 0

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

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

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

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

Simplifying
a = 1
Solution
a = {-2, 1}