(x-6)(x-3)=28

Solution for (x-6)(x-3)=28 equation:

Simplifying
(x + -6)(x + -3) = 28

Reorder the terms:
(-6 + x)(x + -3) = 28

Reorder the terms:
(-6 + x)(-3 + x) = 28

Multiply (-6 + x) * (-3 + x)
(-6(-3 + x) + x(-3 + x)) = 28
((-3 * -6 + x * -6) + x(-3 + x)) = 28
((18 + -6x) + x(-3 + x)) = 28
(18 + -6x + (-3 * x + x * x)) = 28
(18 + -6x + (-3x + x2)) = 28

Combine like terms: -6x + -3x = -9x
(18 + -9x + x2) = 28

Solving
18 + -9x + x2 = 28

Solving for variable 'x'.

Reorder the terms:
18 + -28 + -9x + x2 = 28 + -28

Combine like terms: 18 + -28 = -10
-10 + -9x + x2 = 28 + -28

Combine like terms: 28 + -28 = 0
-10 + -9x + 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}