(x-4)(x-6)=8

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Solution for (x-4)(x-6)=8 equation: 


Simplifying
(x + -4)(x + -6) = 8

Reorder the terms:
(-4 + x)(x + -6) = 8

Reorder the terms:
(-4 + x)(-6 + x) = 8

Multiply (-4 + x) * (-6 + x)
(-4(-6 + x) + x(-6 + x)) = 8
((-6 * -4 + x * -4) + x(-6 + x)) = 8
((24 + -4x) + x(-6 + x)) = 8
(24 + -4x + (-6 * x + x * x)) = 8
(24 + -4x + (-6x + x2)) = 8

Combine like terms: -4x + -6x = -10x
(24 + -10x + x2) = 8

Solving
24 + -10x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
24 + -8 + -10x + x2 = 8 + -8

Combine like terms: 24 + -8 = 16
16 + -10x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
16 + -10x + x2 = 0

Factor a trinomial.
(2 + -1x)(8 + -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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {2, 8}

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