(3x-8)(x-6)=0

Solution for (3x-8)(x-6)=0 equation:

Simplifying
(3x + -8)(x + -6) = 0

Reorder the terms:
(-8 + 3x)(x + -6) = 0

Reorder the terms:
(-8 + 3x)(-6 + x) = 0

Multiply (-8 + 3x) * (-6 + x)
(-8(-6 + x) + 3x * (-6 + x)) = 0
((-6 * -8 + x * -8) + 3x * (-6 + x)) = 0
((48 + -8x) + 3x * (-6 + x)) = 0
(48 + -8x + (-6 * 3x + x * 3x)) = 0
(48 + -8x + (-18x + 3x2)) = 0

Combine like terms: -8x + -18x = -26x
(48 + -26x + 3x2) = 0

Solving
48 + -26x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(8 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 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 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
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 = {2.666666667, 6}