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

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

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

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

Multiply (-9 + 4x) * (6 + -1x)
(-9(6 + -1x) + 4x * (6 + -1x)) = 0
((6 * -9 + -1x * -9) + 4x * (6 + -1x)) = 0
((-54 + 9x) + 4x * (6 + -1x)) = 0
(-54 + 9x + (6 * 4x + -1x * 4x)) = 0
(-54 + 9x + (24x + -4x2)) = 0

Combine like terms: 9x + 24x = 33x
(-54 + 33x + -4x2) = 0

Solving
-54 + 33x + -4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

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

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

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

Simplifying
x = 6
Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -4x = 0 + -9

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

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

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

Simplifying
x = 2.25
Solution
x = {6, 2.25}