(x-2)((x+10)-2)=416

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Solution for (x-2)((x+10)-2)=416 equation: 


Simplifying
(x + -2)((x + 10) + -2) = 416

Reorder the terms:
(-2 + x)((x + 10) + -2) = 416

Reorder the terms:
(-2 + x)((10 + x) + -2) = 416

Remove parenthesis around (10 + x)
(-2 + x)(10 + x + -2) = 416

Reorder the terms:
(-2 + x)(10 + -2 + x) = 416

Combine like terms: 10 + -2 = 8
(-2 + x)(8 + x) = 416

Multiply (-2 + x) * (8 + x)
(-2(8 + x) + x(8 + x)) = 416
((8 * -2 + x * -2) + x(8 + x)) = 416
((-16 + -2x) + x(8 + x)) = 416
(-16 + -2x + (8 * x + x * x)) = 416
(-16 + -2x + (8x + x2)) = 416

Combine like terms: -2x + 8x = 6x
(-16 + 6x + x2) = 416

Solving
-16 + 6x + x2 = 416

Solving for variable 'x'.

Reorder the terms:
-16 + -416 + 6x + x2 = 416 + -416

Combine like terms: -16 + -416 = -432
-432 + 6x + x2 = 416 + -416

Combine like terms: 416 + -416 = 0
-432 + 6x + x2 = 0

Factor a trinomial.
(-24 + -1x)(18 + -1x) = 0


Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-24, 18}

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