(x-2)(x-7)=6

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Solution for (x-2)(x-7)=6 equation: 


Simplifying
(x + -2)(x + -7) = 6

Reorder the terms:
(-2 + x)(x + -7) = 6

Reorder the terms:
(-2 + x)(-7 + x) = 6

Multiply (-2 + x) * (-7 + x)
(-2(-7 + x) + x(-7 + x)) = 6
((-7 * -2 + x * -2) + x(-7 + x)) = 6
((14 + -2x) + x(-7 + x)) = 6
(14 + -2x + (-7 * x + x * x)) = 6
(14 + -2x + (-7x + x2)) = 6

Combine like terms: -2x + -7x = -9x
(14 + -9x + x2) = 6

Solving
14 + -9x + x2 = 6

Solving for variable 'x'.

Reorder the terms:
14 + -6 + -9x + x2 = 6 + -6

Combine like terms: 14 + -6 = 8
8 + -9x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
8 + -9x + x2 = 0

Factor a trinomial.
(1 + -1x)(8 + -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 '(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 = {1, 8}

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