6(2a^2+3a)=6(3-2a)

Solution for 6(2a^2+3a)=6(3-2a) equation:

Simplifying
6(2a2 + 3a) = 6(3 + -2a)

Reorder the terms:
6(3a + 2a2) = 6(3 + -2a)
(3a * 6 + 2a2 * 6) = 6(3 + -2a)
(18a + 12a2) = 6(3 + -2a)
18a + 12a2 = (3 * 6 + -2a * 6)
18a + 12a2 = (18 + -12a)

Solving
18a + 12a2 = 18 + -12a

Solving for variable 'a'.

Reorder the terms:
-18 + 18a + 12a + 12a2 = 18 + -12a + -18 + 12a

Combine like terms: 18a + 12a = 30a
-18 + 30a + 12a2 = 18 + -12a + -18 + 12a

Reorder the terms:
-18 + 30a + 12a2 = 18 + -18 + -12a + 12a

Combine like terms: 18 + -18 = 0
-18 + 30a + 12a2 = 0 + -12a + 12a
-18 + 30a + 12a2 = -12a + 12a

Combine like terms: -12a + 12a = 0
-18 + 30a + 12a2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 5a + 2a2) = 0

Factor a trinomial.
6((-3 + -1a)(1 + -2a)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve:

Simplifying
-3 + -1a = 0

Solving
-3 + -1a = 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 + -1a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1a = 0 + 3
-1a = 0 + 3

Combine like terms: 0 + 3 = 3
-1a = 3

Divide each side by '-1'.
a = -3

Simplifying
a = -3
Subproblem 2
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
Solution
a = {-3, 0.5}