(x-6)(8-x)=0

Solution for (x-6)(8-x)=0 equation:

Simplifying
(x + -6)(8 + -1x) = 0

Reorder the terms:
(-6 + x)(8 + -1x) = 0

Multiply (-6 + x) * (8 + -1x)
(-6(8 + -1x) + x(8 + -1x)) = 0
((8 * -6 + -1x * -6) + x(8 + -1x)) = 0
((-48 + 6x) + x(8 + -1x)) = 0
(-48 + 6x + (8 * x + -1x * x)) = 0
(-48 + 6x + (8x + -1x2)) = 0

Combine like terms: 6x + 8x = 14x
(-48 + 14x + -1x2) = 0

Solving
-48 + 14x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-8 + x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {8, 6}