(x-4)(-1-x)-6=0

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Solution for (x-4)(-1-x)-6=0 equation:


Simplifying
(x + -4)(-1 + -1x) + -6 = 0

Reorder the terms:
(-4 + x)(-1 + -1x) + -6 = 0

Multiply (-4 + x) * (-1 + -1x)
(-4(-1 + -1x) + x(-1 + -1x)) + -6 = 0
((-1 * -4 + -1x * -4) + x(-1 + -1x)) + -6 = 0
((4 + 4x) + x(-1 + -1x)) + -6 = 0
(4 + 4x + (-1 * x + -1x * x)) + -6 = 0
(4 + 4x + (-1x + -1x2)) + -6 = 0

Combine like terms: 4x + -1x = 3x
(4 + 3x + -1x2) + -6 = 0

Reorder the terms:
4 + -6 + 3x + -1x2 = 0

Combine like terms: 4 + -6 = -2
-2 + 3x + -1x2 = 0

Solving
-2 + 3x + -1x2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 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 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

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 = {2, 1}

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