x-2=x^2+3x-17

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Solution for x-2=x^2+3x-17 equation: 


Simplifying
x + -2 = x2 + 3x + -17

Reorder the terms:
-2 + x = x2 + 3x + -17

Reorder the terms:
-2 + x = -17 + 3x + x2

Solving
-2 + x = -17 + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-2 + 17 + x + -3x + -1x2 = -17 + 3x + x2 + 17 + -3x + -1x2

Combine like terms: -2 + 17 = 15
15 + x + -3x + -1x2 = -17 + 3x + x2 + 17 + -3x + -1x2

Combine like terms: x + -3x = -2x
15 + -2x + -1x2 = -17 + 3x + x2 + 17 + -3x + -1x2

Reorder the terms:
15 + -2x + -1x2 = -17 + 17 + 3x + -3x + x2 + -1x2

Combine like terms: -17 + 17 = 0
15 + -2x + -1x2 = 0 + 3x + -3x + x2 + -1x2
15 + -2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
15 + -2x + -1x2 = 0 + x2 + -1x2
15 + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
15 + -2x + -1x2 = 0

Factor a trinomial.
(3 + -1x)(5 + x) = 0


Subproblem 1
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

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 = {3, -5}

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