x^2-2x-17=-5x+1

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Solution for x^2-2x-17=-5x+1 equation: 


Simplifying
x2 + -2x + -17 = -5x + 1

Reorder the terms:
-17 + -2x + x2 = -5x + 1

Reorder the terms:
-17 + -2x + x2 = 1 + -5x

Solving
-17 + -2x + x2 = 1 + -5x

Solving for variable 'x'.

Reorder the terms:
-17 + -1 + -2x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -17 + -1 = -18
-18 + -2x + 5x + x2 = 1 + -5x + -1 + 5x

Combine like terms: -2x + 5x = 3x
-18 + 3x + x2 = 1 + -5x + -1 + 5x

Reorder the terms:
-18 + 3x + x2 = 1 + -1 + -5x + 5x

Combine like terms: 1 + -1 = 0
-18 + 3x + x2 = 0 + -5x + 5x
-18 + 3x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-18 + 3x + x2 = 0

Factor a trinomial.
(-6 + -1x)(3 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

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

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

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}

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