(a+3)*(2a-1)=15

Solution for (a+3)*(2a-1)=15 equation:

Simplifying
(a + 3)(2a + -1) = 15

Reorder the terms:
(3 + a)(2a + -1) = 15

Reorder the terms:
(3 + a)(-1 + 2a) = 15

Multiply (3 + a) * (-1 + 2a)
(3(-1 + 2a) + a(-1 + 2a)) = 15
((-1 * 3 + 2a * 3) + a(-1 + 2a)) = 15
((-3 + 6a) + a(-1 + 2a)) = 15
(-3 + 6a + (-1 * a + 2a * a)) = 15
(-3 + 6a + (-1a + 2a2)) = 15

Combine like terms: 6a + -1a = 5a
(-3 + 5a + 2a2) = 15

Solving
-3 + 5a + 2a2 = 15

Solving for variable 'a'.

Reorder the terms:
-3 + -15 + 5a + 2a2 = 15 + -15

Combine like terms: -3 + -15 = -18
-18 + 5a + 2a2 = 15 + -15

Combine like terms: 15 + -15 = 0
-18 + 5a + 2a2 = 0

Factor a trinomial.
(-9 + -2a)(2 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a = 0 + 9
-2a = 0 + 9

Combine like terms: 0 + 9 = 9
-2a = 9

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5
Subproblem 2
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
Solution
a = {-4.5, 2}