(x-6)(x-10)=32

Solution for (x-6)(x-10)=32 equation:

Simplifying
(x + -6)(x + -10) = 32

Reorder the terms:
(-6 + x)(x + -10) = 32

Reorder the terms:
(-6 + x)(-10 + x) = 32

Multiply (-6 + x) * (-10 + x)
(-6(-10 + x) + x(-10 + x)) = 32
((-10 * -6 + x * -6) + x(-10 + x)) = 32
((60 + -6x) + x(-10 + x)) = 32
(60 + -6x + (-10 * x + x * x)) = 32
(60 + -6x + (-10x + x2)) = 32

Combine like terms: -6x + -10x = -16x
(60 + -16x + x2) = 32

Solving
60 + -16x + x2 = 32

Solving for variable 'x'.

Reorder the terms:
60 + -32 + -16x + x2 = 32 + -32

Combine like terms: 60 + -32 = 28
28 + -16x + x2 = 32 + -32

Combine like terms: 32 + -32 = 0
28 + -16x + x2 = 0

Factor a trinomial.
(2 + -1x)(14 + -1x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve:

Simplifying
14 + -1x = 0

Solving
14 + -1x = 0

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

Add '-14' to each side of the equation.
14 + -14 + -1x = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -1x = 0 + -14
-1x = 0 + -14

Combine like terms: 0 + -14 = -14
-1x = -14

Divide each side by '-1'.
x = 14

Simplifying
x = 14
Solution
x = {2, 14}