(x-6)(x-5)=20

Solution for (x-6)(x-5)=20 equation:

Simplifying
(x + -6)(x + -5) = 20

Reorder the terms:
(-6 + x)(x + -5) = 20

Reorder the terms:
(-6 + x)(-5 + x) = 20

Multiply (-6 + x) * (-5 + x)
(-6(-5 + x) + x(-5 + x)) = 20
((-5 * -6 + x * -6) + x(-5 + x)) = 20
((30 + -6x) + x(-5 + x)) = 20
(30 + -6x + (-5 * x + x * x)) = 20
(30 + -6x + (-5x + x2)) = 20

Combine like terms: -6x + -5x = -11x
(30 + -11x + x2) = 20

Solving
30 + -11x + x2 = 20

Solving for variable 'x'.

Reorder the terms:
30 + -20 + -11x + x2 = 20 + -20

Combine like terms: 30 + -20 = 10
10 + -11x + x2 = 20 + -20

Combine like terms: 20 + -20 = 0
10 + -11x + x2 = 0

Factor a trinomial.
(1 + -1x)(10 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {1, 10}