12-4x-x^2=2-x

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Solution for 12-4x-x^2=2-x equation:


Simplifying
12 + -4x + -1x2 = 2 + -1x

Solving
12 + -4x + -1x2 = 2 + -1x

Solving for variable 'x'.

Reorder the terms:
12 + -2 + -4x + x + -1x2 = 2 + -1x + -2 + x

Combine like terms: 12 + -2 = 10
10 + -4x + x + -1x2 = 2 + -1x + -2 + x

Combine like terms: -4x + x = -3x
10 + -3x + -1x2 = 2 + -1x + -2 + x

Reorder the terms:
10 + -3x + -1x2 = 2 + -2 + -1x + x

Combine like terms: 2 + -2 = 0
10 + -3x + -1x2 = 0 + -1x + x
10 + -3x + -1x2 = -1x + x

Combine like terms: -1x + x = 0
10 + -3x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(5 + x) = 0

Subproblem 1

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {2, -5}

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