(x-10)(x-2)=0

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Solution for (x-10)(x-2)=0 equation: 


Simplifying
(x + -10)(x + -2) = 0

Reorder the terms:
(-10 + x)(x + -2) = 0

Reorder the terms:
(-10 + x)(-2 + x) = 0

Multiply (-10 + x) * (-2 + x)
(-10(-2 + x) + x(-2 + x)) = 0
((-2 * -10 + x * -10) + x(-2 + x)) = 0
((20 + -10x) + x(-2 + x)) = 0
(20 + -10x + (-2 * x + x * x)) = 0
(20 + -10x + (-2x + x2)) = 0

Combine like terms: -10x + -2x = -12x
(20 + -12x + x2) = 0

Solving
20 + -12x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -1x)(10 + -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 '(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 = {2, 10}

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