2x-3=9-6x+x^2

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Solution for 2x-3=9-6x+x^2 equation: 


Simplifying
2x + -3 = 9 + -6x + x2

Reorder the terms:
-3 + 2x = 9 + -6x + x2

Solving
-3 + 2x = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -9 + 2x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: -3 + -9 = -12
-12 + 2x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 2x + 6x = 8x
-12 + 8x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-12 + 8x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-12 + 8x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-12 + 8x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-12 + 8x + -1x2 = 0 + x2 + -1x2
-12 + 8x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12 + 8x + -1x2 = 0

Factor a trinomial.
(-6 + x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6

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 = {6, 2}

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