x^2-9x+32=3x+5

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Solution for x^2-9x+32=3x+5 equation: 


Simplifying
x2 + -9x + 32 = 3x + 5

Reorder the terms:
32 + -9x + x2 = 3x + 5

Reorder the terms:
32 + -9x + x2 = 5 + 3x

Solving
32 + -9x + x2 = 5 + 3x

Solving for variable 'x'.

Reorder the terms:
32 + -5 + -9x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: 32 + -5 = 27
27 + -9x + -3x + x2 = 5 + 3x + -5 + -3x

Combine like terms: -9x + -3x = -12x
27 + -12x + x2 = 5 + 3x + -5 + -3x

Reorder the terms:
27 + -12x + x2 = 5 + -5 + 3x + -3x

Combine like terms: 5 + -5 = 0
27 + -12x + x2 = 0 + 3x + -3x
27 + -12x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
27 + -12x + x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}

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