x^2-2x-9=3x+5

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Solution for x^2-2x-9=3x+5 equation: 


Simplifying
x2 + -2x + -9 = 3x + 5

Reorder the terms:
-9 + -2x + x2 = 3x + 5

Reorder the terms:
-9 + -2x + x2 = 5 + 3x

Solving
-9 + -2x + x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
-9 + -5 + -2x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -9 + -5 = -14
-14 + -2x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -2x + -3x = -5x
-14 + -5x + x2 = 5 + 3x + -5 + -3x

Reorder the terms:
-14 + -5x + x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
-14 + -5x + x2 = 0 + 3x + -3x
-14 + -5x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-14 + -5x + x2 = 0

Factor a trinomial.
(-2 + -1x)(7 + -1x) = 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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-2, 7}

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