(2a-3)(4a+6+9)=

Solution for (2a-3)(4a+6+9)= equation:

Simplifying
(2a + -3)(4a + 6 + 9) = 0

Reorder the terms:
(-3 + 2a)(4a + 6 + 9) = 0

Reorder the terms:
(-3 + 2a)(6 + 9 + 4a) = 0

Combine like terms: 6 + 9 = 15
(-3 + 2a)(15 + 4a) = 0

Multiply (-3 + 2a) * (15 + 4a)
(-3(15 + 4a) + 2a * (15 + 4a)) = 0
((15 * -3 + 4a * -3) + 2a * (15 + 4a)) = 0
((-45 + -12a) + 2a * (15 + 4a)) = 0
(-45 + -12a + (15 * 2a + 4a * 2a)) = 0
(-45 + -12a + (30a + 8a2)) = 0

Combine like terms: -12a + 30a = 18a
(-45 + 18a + 8a2) = 0

Solving
-45 + 18a + 8a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-15 + -4a)(3 + -2a) = 0

Subproblem 1
Set the factor '(-15 + -4a)' equal to zero and attempt to solve:

Simplifying
-15 + -4a = 0

Solving
-15 + -4a = 0

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

Add '15' to each side of the equation.
-15 + 15 + -4a = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4a = 0 + 15
-4a = 0 + 15

Combine like terms: 0 + 15 = 15
-4a = 15

Divide each side by '-4'.
a = -3.75

Simplifying
a = -3.75
Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve:

Simplifying
3 + -2a = 0

Solving
3 + -2a = 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 + -2a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2a = 0 + -3
-2a = 0 + -3

Combine like terms: 0 + -3 = -3
-2a = -3

Divide each side by '-2'.
a = 1.5

Simplifying
a = 1.5
Solution
a = {-3.75, 1.5}