(a-3)(4a+9)=0

Solution for (a-3)(4a+9)=0 equation:

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

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

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

Multiply (-3 + a) * (9 + 4a)
(-3(9 + 4a) + a(9 + 4a)) = 0
((9 * -3 + 4a * -3) + a(9 + 4a)) = 0
((-27 + -12a) + a(9 + 4a)) = 0
(-27 + -12a + (9 * a + 4a * a)) = 0
(-27 + -12a + (9a + 4a2)) = 0

Combine like terms: -12a + 9a = -3a
(-27 + -3a + 4a2) = 0

Solving
-27 + -3a + 4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-9 + -4a)(3 + -1a) = 0

Subproblem 1
Set the factor '(-9 + -4a)' equal to zero and attempt to solve:

Simplifying
-9 + -4a = 0

Solving
-9 + -4a = 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 + -4a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4a = 0 + 9
-4a = 0 + 9

Combine like terms: 0 + 9 = 9
-4a = 9

Divide each side by '-4'.
a = -2.25

Simplifying
a = -2.25
Subproblem 2
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
Solution
a = {-2.25, 3}