(x-6)(x-3)=-2

Solution for (x-6)(x-3)=-2 equation:

Simplifying
(x + -6)(x + -3) = -2

Reorder the terms:
(-6 + x)(x + -3) = -2

Reorder the terms:
(-6 + x)(-3 + x) = -2

Multiply (-6 + x) * (-3 + x)
(-6(-3 + x) + x(-3 + x)) = -2
((-3 * -6 + x * -6) + x(-3 + x)) = -2
((18 + -6x) + x(-3 + x)) = -2
(18 + -6x + (-3 * x + x * x)) = -2
(18 + -6x + (-3x + x2)) = -2

Combine like terms: -6x + -3x = -9x
(18 + -9x + x2) = -2

Solving
18 + -9x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
18 + 2 + -9x + x2 = -2 + 2

Combine like terms: 18 + 2 = 20
20 + -9x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
20 + -9x + x2 = 0

Factor a trinomial.
(4 + -1x)(5 + -1x) = 0

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
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 = {4, 5}