(2x-5)(6-x)=0

Solution for (2x-5)(6-x)=0 equation:

Simplifying
(2x + -5)(6 + -1x) = 0

Reorder the terms:
(-5 + 2x)(6 + -1x) = 0

Multiply (-5 + 2x) * (6 + -1x)
(-5(6 + -1x) + 2x * (6 + -1x)) = 0
((6 * -5 + -1x * -5) + 2x * (6 + -1x)) = 0
((-30 + 5x) + 2x * (6 + -1x)) = 0
(-30 + 5x + (6 * 2x + -1x * 2x)) = 0
(-30 + 5x + (12x + -2x2)) = 0

Combine like terms: 5x + 12x = 17x
(-30 + 17x + -2x2) = 0

Solving
-30 + 17x + -2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(5 + -2x) = 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 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 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 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {6, 2.5}