(x-3)(x-8)-6=0

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Solution for (x-3)(x-8)-6=0 equation:


Simplifying
(x + -3)(x + -8) + -6 = 0

Reorder the terms:
(-3 + x)(x + -8) + -6 = 0

Reorder the terms:
(-3 + x)(-8 + x) + -6 = 0

Multiply (-3 + x) * (-8 + x)
(-3(-8 + x) + x(-8 + x)) + -6 = 0
((-8 * -3 + x * -3) + x(-8 + x)) + -6 = 0
((24 + -3x) + x(-8 + x)) + -6 = 0
(24 + -3x + (-8 * x + x * x)) + -6 = 0
(24 + -3x + (-8x + x2)) + -6 = 0

Combine like terms: -3x + -8x = -11x
(24 + -11x + x2) + -6 = 0

Reorder the terms:
24 + -6 + -11x + x2 = 0

Combine like terms: 24 + -6 = 18
18 + -11x + x2 = 0

Solving
18 + -11x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {2, 9}

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