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

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

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

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

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

Multiply (-6 + x) * (-5 + 6x)
(-6(-5 + 6x) + x(-5 + 6x)) = 0
((-5 * -6 + 6x * -6) + x(-5 + 6x)) = 0
((30 + -36x) + x(-5 + 6x)) = 0
(30 + -36x + (-5 * x + 6x * x)) = 0
(30 + -36x + (-5x + 6x2)) = 0

Combine like terms: -36x + -5x = -41x
(30 + -41x + 6x2) = 0

Solving
30 + -41x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -6x)(6 + -1x) = 0

Subproblem 1
Set the factor '(5 + -6x)' equal to zero and attempt to solve:

Simplifying
5 + -6x = 0

Solving
5 + -6x = 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 + -6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6x = 0 + -5
-6x = 0 + -5

Combine like terms: 0 + -5 = -5
-6x = -5

Divide each side by '-6'.
x = 0.8333333333

Simplifying
x = 0.8333333333
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 = {0.8333333333, 6}