x^2-3x+8=2x+22

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Solution for x^2-3x+8=2x+22 equation: 


Simplifying
x2 + -3x + 8 = 2x + 22

Reorder the terms:
8 + -3x + x2 = 2x + 22

Reorder the terms:
8 + -3x + x2 = 22 + 2x

Solving
8 + -3x + x2 = 22 + 2x

Solving for variable 'x'.

Reorder the terms:
8 + -22 + -3x + -2x + x2 = 22 + 2x + -22 + -2x

Combine like terms: 8 + -22 = -14
-14 + -3x + -2x + x2 = 22 + 2x + -22 + -2x

Combine like terms: -3x + -2x = -5x
-14 + -5x + x2 = 22 + 2x + -22 + -2x

Reorder the terms:
-14 + -5x + x2 = 22 + -22 + 2x + -2x

Combine like terms: 22 + -22 = 0
-14 + -5x + x2 = 0 + 2x + -2x
-14 + -5x + x2 = 2x + -2x

Combine like terms: 2x + -2x = 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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