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

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

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

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

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

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

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

Solving
-3 + 7a + 6a2 = 2

Solving for variable 'a'.

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

Combine like terms: -3 + -2 = -5
-5 + 7a + 6a2 = 2 + -2

Combine like terms: 2 + -2 = 0
-5 + 7a + 6a2 = 0

Factor a trinomial.
(-5 + -3a)(1 + -2a) = 0

Subproblem 1
Set the factor '(-5 + -3a)' equal to zero and attempt to solve:

Simplifying
-5 + -3a = 0

Solving
-5 + -3a = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3a = 0 + 5
-3a = 0 + 5

Combine like terms: 0 + 5 = 5
-3a = 5

Divide each side by '-3'.
a = -1.666666667

Simplifying
a = -1.666666667
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 = {-1.666666667, 0.5}