(-1-x)(2x-8)=0

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Solution for (-1-x)(2x-8)=0 equation: 


Simplifying
(-1 + -1x)(2x + -8) = 0

Reorder the terms:
(-1 + -1x)(-8 + 2x) = 0

Multiply (-1 + -1x) * (-8 + 2x)
(-1(-8 + 2x) + -1x * (-8 + 2x)) = 0
((-8 * -1 + 2x * -1) + -1x * (-8 + 2x)) = 0
((8 + -2x) + -1x * (-8 + 2x)) = 0
(8 + -2x + (-8 * -1x + 2x * -1x)) = 0
(8 + -2x + (8x + -2x2)) = 0

Combine like terms: -2x + 8x = 6x
(8 + 6x + -2x2) = 0

Solving
8 + 6x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(1 + x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

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

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

Simplifying
x = -1
Solution
x = {4, -1}

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