(4x-5)(6-x)=

Solution for (4x-5)(6-x)= equation:

Simplifying
(4x + -5)(6 + -1x) = 0

Reorder the terms:
(-5 + 4x)(6 + -1x) = 0

Multiply (-5 + 4x) * (6 + -1x)
(-5(6 + -1x) + 4x * (6 + -1x)) = 0
((6 * -5 + -1x * -5) + 4x * (6 + -1x)) = 0
((-30 + 5x) + 4x * (6 + -1x)) = 0
(-30 + 5x + (6 * 4x + -1x * 4x)) = 0
(-30 + 5x + (24x + -4x2)) = 0

Combine like terms: 5x + 24x = 29x
(-30 + 29x + -4x2) = 0

Solving
-30 + 29x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(5 + -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 '(5 + -4x)' equal to zero and attempt to solve:

Simplifying
5 + -4x = 0

Solving
5 + -4x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -4x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4x = 0 + -5
-4x = 0 + -5

Combine like terms: 0 + -5 = -5
-4x = -5

Divide each side by '-4'.
x = 1.25

Simplifying
x = 1.25
Solution
x = {6, 1.25}