(x-3)(x-10)=8

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Solution for (x-3)(x-10)=8 equation: 


Simplifying
(x + -3)(x + -10) = 8

Reorder the terms:
(-3 + x)(x + -10) = 8

Reorder the terms:
(-3 + x)(-10 + x) = 8

Multiply (-3 + x) * (-10 + x)
(-3(-10 + x) + x(-10 + x)) = 8
((-10 * -3 + x * -3) + x(-10 + x)) = 8
((30 + -3x) + x(-10 + x)) = 8
(30 + -3x + (-10 * x + x * x)) = 8
(30 + -3x + (-10x + x2)) = 8

Combine like terms: -3x + -10x = -13x
(30 + -13x + x2) = 8

Solving
30 + -13x + x2 = 8

Solving for variable 'x'.

Reorder the terms:
30 + -8 + -13x + x2 = 8 + -8

Combine like terms: 30 + -8 = 22
22 + -13x + x2 = 8 + -8

Combine like terms: 8 + -8 = 0
22 + -13x + x2 = 0

Factor a trinomial.
(2 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {2, 11}

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