6x=x^2-12x+32

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Solution for 6x=x^2-12x+32 equation: 


Simplifying
6x = x2 + -12x + 32

Reorder the terms:
6x = 32 + -12x + x2

Solving
6x = 32 + -12x + x2

Solving for variable 'x'.

Reorder the terms:
-32 + 6x + 12x + -1x2 = 32 + -12x + x2 + -32 + 12x + -1x2

Combine like terms: 6x + 12x = 18x
-32 + 18x + -1x2 = 32 + -12x + x2 + -32 + 12x + -1x2

Reorder the terms:
-32 + 18x + -1x2 = 32 + -32 + -12x + 12x + x2 + -1x2

Combine like terms: 32 + -32 = 0
-32 + 18x + -1x2 = 0 + -12x + 12x + x2 + -1x2
-32 + 18x + -1x2 = -12x + 12x + x2 + -1x2

Combine like terms: -12x + 12x = 0
-32 + 18x + -1x2 = 0 + x2 + -1x2
-32 + 18x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-32 + 18x + -1x2 = 0

Factor a trinomial.
(-16 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-16 + x)' equal to zero and attempt to solve:

Simplifying
-16 + x = 0

Solving
-16 + x = 0

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

Add '16' to each side of the equation.
-16 + 16 + x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + x = 0 + 16
x = 0 + 16

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16

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 = {16, 2}

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