2x-5=x^2+6x-17

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Solution for 2x-5=x^2+6x-17 equation: 


Simplifying
2x + -5 = x2 + 6x + -17

Reorder the terms:
-5 + 2x = x2 + 6x + -17

Reorder the terms:
-5 + 2x = -17 + 6x + x2

Solving
-5 + 2x = -17 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
-5 + 17 + 2x + -6x + -1x2 = -17 + 6x + x2 + 17 + -6x + -1x2

Combine like terms: -5 + 17 = 12
12 + 2x + -6x + -1x2 = -17 + 6x + x2 + 17 + -6x + -1x2

Combine like terms: 2x + -6x = -4x
12 + -4x + -1x2 = -17 + 6x + x2 + 17 + -6x + -1x2

Reorder the terms:
12 + -4x + -1x2 = -17 + 17 + 6x + -6x + x2 + -1x2

Combine like terms: -17 + 17 = 0
12 + -4x + -1x2 = 0 + 6x + -6x + x2 + -1x2
12 + -4x + -1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
12 + -4x + -1x2 = 0 + x2 + -1x2
12 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -4x + -1x2 = 0

Factor a trinomial.
(2 + -1x)(6 + 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {2, -6}

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