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

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

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

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

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

Multiply (-5 + x) * (-6 + 5x)
(-5(-6 + 5x) + x(-6 + 5x)) = 0
((-6 * -5 + 5x * -5) + x(-6 + 5x)) = 0
((30 + -25x) + x(-6 + 5x)) = 0
(30 + -25x + (-6 * x + 5x * x)) = 0
(30 + -25x + (-6x + 5x2)) = 0

Combine like terms: -25x + -6x = -31x
(30 + -31x + 5x2) = 0

Solving
30 + -31x + 5x2 = 0

Solving for variable 'x'.

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

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

Simplifying
6 + -5x = 0

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

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

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

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.2, 5}