x^2+3x-17=2x-5

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Solution for x^2+3x-17=2x-5 equation: 


Simplifying
x2 + 3x + -17 = 2x + -5

Reorder the terms:
-17 + 3x + x2 = 2x + -5

Reorder the terms:
-17 + 3x + x2 = -5 + 2x

Solving
-17 + 3x + x2 = -5 + 2x

Solving for variable 'x'.

Reorder the terms:
-17 + 5 + 3x + -2x + x2 = -5 + 2x + 5 + -2x

Combine like terms: -17 + 5 = -12
-12 + 3x + -2x + x2 = -5 + 2x + 5 + -2x

Combine like terms: 3x + -2x = 1x
-12 + 1x + x2 = -5 + 2x + 5 + -2x

Reorder the terms:
-12 + 1x + x2 = -5 + 5 + 2x + -2x

Combine like terms: -5 + 5 = 0
-12 + 1x + x2 = 0 + 2x + -2x
-12 + 1x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + 1x + x2 = 0

Factor a trinomial.
(-4 + -1x)(3 + -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 '(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 = {-4, 3}

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