x^2-5x+14=3x+2

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Solution for x^2-5x+14=3x+2 equation: 


Simplifying
x2 + -5x + 14 = 3x + 2

Reorder the terms:
14 + -5x + x2 = 3x + 2

Reorder the terms:
14 + -5x + x2 = 2 + 3x

Solving
14 + -5x + x2 = 2 + 3x

Solving for variable 'x'.

Reorder the terms:
14 + -2 + -5x + -3x + x2 = 2 + 3x + -2 + -3x

Combine like terms: 14 + -2 = 12
12 + -5x + -3x + x2 = 2 + 3x + -2 + -3x

Combine like terms: -5x + -3x = -8x
12 + -8x + x2 = 2 + 3x + -2 + -3x

Reorder the terms:
12 + -8x + x2 = 2 + -2 + 3x + -3x

Combine like terms: 2 + -2 = 0
12 + -8x + x2 = 0 + 3x + -3x
12 + -8x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -8x + x2 = 0

Factor a trinomial.
(2 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {2, 6}

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