1x(8-x)=8-x

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Solution for 1x(8-x)=8-x equation: 


Simplifying
1x(8 + -1x) = 8 + -1x
(8 * 1x + -1x * 1x) = 8 + -1x
(8x + -1x2) = 8 + -1x

Solving
8x + -1x2 = 8 + -1x

Solving for variable 'x'.

Reorder the terms:
-8 + 8x + x + -1x2 = 8 + -1x + -8 + x

Combine like terms: 8x + x = 9x
-8 + 9x + -1x2 = 8 + -1x + -8 + x

Reorder the terms:
-8 + 9x + -1x2 = 8 + -8 + -1x + x

Combine like terms: 8 + -8 = 0
-8 + 9x + -1x2 = 0 + -1x + x
-8 + 9x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
-8 + 9x + -1x2 = 0

Factor a trinomial.
(-8 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 0

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

Add '8' to each side of the equation.
-8 + 8 + x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + x = 0 + 8
x = 0 + 8

Combine like terms: 0 + 8 = 8
x = 8

Simplifying
x = 8

Subproblem 2
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
Solution
x = {8, 1}

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