(x-9)(x-2)=8

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Solution for (x-9)(x-2)=8 equation: 


Simplifying
(x + -9)(x + -2) = 8

Reorder the terms:
(-9 + x)(x + -2) = 8

Reorder the terms:
(-9 + x)(-2 + x) = 8

Multiply (-9 + x) * (-2 + x)
(-9(-2 + x) + x(-2 + x)) = 8
((-2 * -9 + x * -9) + x(-2 + x)) = 8
((18 + -9x) + x(-2 + x)) = 8
(18 + -9x + (-2 * x + x * x)) = 8
(18 + -9x + (-2x + x2)) = 8

Combine like terms: -9x + -2x = -11x
(18 + -11x + x2) = 8

Solving
18 + -11x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
18 + -8 + -11x + x2 = 8 + -8

Combine like terms: 18 + -8 = 10
10 + -11x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
10 + -11x + 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}

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