(4a-9)(6-a)=0

Solution for (4a-9)(6-a)=0 equation:

Simplifying
(4a + -9)(6 + -1a) = 0

Reorder the terms:
(-9 + 4a)(6 + -1a) = 0

Multiply (-9 + 4a) * (6 + -1a)
(-9(6 + -1a) + 4a * (6 + -1a)) = 0
((6 * -9 + -1a * -9) + 4a * (6 + -1a)) = 0
((-54 + 9a) + 4a * (6 + -1a)) = 0
(-54 + 9a + (6 * 4a + -1a * 4a)) = 0
(-54 + 9a + (24a + -4a2)) = 0

Combine like terms: 9a + 24a = 33a
(-54 + 33a + -4a2) = 0

Solving
-54 + 33a + -4a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + a)(9 + -4a) = 0

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

Simplifying
-6 + a = 0

Solving
-6 + a = 0

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

Add '6' to each side of the equation.
-6 + 6 + a = 0 + 6

Combine like terms: -6 + 6 = 0
0 + a = 0 + 6
a = 0 + 6

Combine like terms: 0 + 6 = 6
a = 6

Simplifying
a = 6
Subproblem 2
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
Solution
a = {6, 2.25}