x^2-2x-16=4-x

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Solution for x^2-2x-16=4-x equation:


Simplifying
x2 + -2x + -16 = 4 + -1x

Reorder the terms:
-16 + -2x + x2 = 4 + -1x

Solving
-16 + -2x + x2 = 4 + -1x

Solving for variable 'x'.

Reorder the terms:
-16 + -4 + -2x + x + x2 = 4 + -1x + -4 + x

Combine like terms: -16 + -4 = -20
-20 + -2x + x + x2 = 4 + -1x + -4 + x

Combine like terms: -2x + x = -1x
-20 + -1x + x2 = 4 + -1x + -4 + x

Reorder the terms:
-20 + -1x + x2 = 4 + -4 + -1x + x

Combine like terms: 4 + -4 = 0
-20 + -1x + x2 = 0 + -1x + x
-20 + -1x + x2 = -1x + x

Combine like terms: -1x + x = 0
-20 + -1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(5 + -1x) = 0

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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-4, 5}

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