x^2+6x-17=3x-7

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Solution for x^2+6x-17=3x-7 equation: 


Simplifying
x2 + 6x + -17 = 3x + -7

Reorder the terms:
-17 + 6x + x2 = 3x + -7

Reorder the terms:
-17 + 6x + x2 = -7 + 3x

Solving
-17 + 6x + x2 = -7 + 3x

Solving for variable 'x'.

Reorder the terms:
-17 + 7 + 6x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: -17 + 7 = -10
-10 + 6x + -3x + x2 = -7 + 3x + 7 + -3x

Combine like terms: 6x + -3x = 3x
-10 + 3x + x2 = -7 + 3x + 7 + -3x

Reorder the terms:
-10 + 3x + x2 = -7 + 7 + 3x + -3x

Combine like terms: -7 + 7 = 0
-10 + 3x + x2 = 0 + 3x + -3x
-10 + 3x + x2 = 3x + -3x

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

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


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 2}

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